new linear codes from 040509

• binary: 1 optimal + 4 improvement + 5 derived
• ternary:1 optimal + 1 optimal derived + 2 derived
• q=4 : 11 improvements + 15 derived
• q=5:
• q=7:
• q=8:
• q=9:

binary q=2

q=2 k=11 n=168 d=78 
(extension of a code using automorphisms)
( link )

generator matrix:
000111111111110000000111111100000000000111100000000111111100111000000001111111000000011111111000000001111111000000011111111000000000011110000000011111110000000000011111
111000000111110011111000111100000011111011100001111011111101001000001110011111000001100001111000000010011111001111100011111000001111100110001111100000010000001111100010
011000001011110100001011011100111100111000100110001100111100011000010110101111000010000110001000111100100111000001111100111000110011100010010000100001100111110011100000
101001111101111101111001001111001111001000111010000101111101101001100010110011001110000000111011001101111001110010100101000001011101100100110001100111111011110101101101
110010111000111100110111111100010101011000101110011110001101101111100101011100000000101110110100010000001000111101111110011001000010001001000010000000101001111110111111
011011011010110011111101100101000011001001111001110011000011100000100010100101000010000110001011101100010111010100101011000111001100011101001100000001100100010100010111
000111100010111101000011110110110110111111100110111001000111100010001110100011010111100001011100110001100110000111000010000011100110000000010101000000001110101001100011
110010001000011111011111110111101010000100010011000000011101100010100101010100001010110010100101110111111011101111110111101111111010111101110110111111100111111111101100
110101001011011100011011100101111101100011100011010111011100100101011101010011110011110101011111100000101001010101111101000111101011000101110000101000111001010011100111
000010111010101001111001100011011001110010000010111000111000111111101001011111011000000000011011110011000001010001101011101101001011111100001011001011011011101011000011
110100111000110011011000101001000001000101001101111011010110001011010101010011100110100011000100001110100001000101001101001101111100110001101000100101000111001111101010
mindist=78
weight enumerator=1 [0]  711 [78]  307 [80]  515 [86]  145 [88]  293 [94]  56 [96]  17 [102
]  3 [104]  

q=2 k=11 n=171 d=80 optimal
(extension of a code using automorphisms)
( link )

generator matrix:
000011111111111000000011111111000000000001111000000001111111001110000000011111110000000111111110000000011111110000000111111110000000000111110000000011111110000000000011111
011100000011111001111100011111000000111110111000011110111111010010000011100111110000011000011110000000100111110011111000111110000011111001110001111100000010000001111100010
101100000101111010000101101111001111001110001001100011001111000110000101101011110000100001100010001111001001110000011111001110001100111000010010000100001100111110011100000
110100111110111110111100100111110011110010001110100001011111011010011000101100110011100000001110110011011110011100101001010000010111011000100110001100111111011110101101101
111001011100011110011011111111000101010110001011100111100011011011111001010111000000001011101101000100000010001111011111100110010000100010001000010000000101001111110111111
001101101101011001111110110011010000110010011110011100110000111000001000101001010000100001100010111011000101110101001010110001110011000111101001100000001100100010100010111
000011110001011110100001111001101101101111111001101110010001111000100011101000110101111000010111001100011001100001110000100000111001100000000010101000000001110101001100011
111001000100001111101111111001111010100001000100110000000111011000101001010101000010101100101001011101111110111011111101111011111110101111101110110111111100111111111101100
111010100101101110001101110001011111011000111000110101110111001001010111010100111100111101010111111000001010010101011111010001111010110001101110000101000111001010011100111
100001011101010100111100110010110110011100100000101110001110001111111010010111110110000000000110111100110000010100011010111011010010111110100001011001011011011101011000011
011010011100011001101100010100010000010001010011011110110101100010110101010100111001101000110001000011101000010001010011010011011111001100001101000100101000111001111101010
mindist=80
weight enumerator=1 [0]  1018 [80]  660 [88]  349 [96]  20 [104]  
This is a self-orthogonal code

q=2 k=11 n=248 d=118
(extension of a code using automorphisms)
( link )

generator matrix:
00000000001111111110000000001111111110000000001111111110000000000111111110000111110000000001111111110000111110000000001111111110000001111111111110000011110001111110000000001111111110000001110000000000001111110000000110100000011111010010000100111100
00001111110001111110000000110011111110000001110001111110000011111000011111111001110000011110000111110111000010001111110001111110001110000001111110001100010010011110000111110000111110001110110000001111110001110011111011100111101101100100000110011010
00010000110010000110001111010100011110000111111110000110000100001000100010001000010001101110111000110001001110000001110000001110010010001110001110010111110100001110111000110111000110010010110011110011110110110101111011111001110100110000001011100101
00110011110110011110110111101001101110111010110110111010000100001011101110111000010110100010001011010111010110000010010000010010110110110110110111111000110110110111001001011001001010110100010000010000011001001110001000000000101000000000110010010101
00010101000010101000111011101001110111001111011011001110011000110011101111000010110000110111011000010011110110111110110111110110010010010010010011100101111011011011110011001110011000101110000111110111111011010000111011100010010011000000010101010011
00011000000011000001011001111110110011010110000001010111100111001000100010001010111011110011001101111010101110000110110000110111001000101010101010001001001000011101011110011011110011110110100100010100011011011011001110000100101100000000111001110000
00111000010111000011100111010111001110100111001000100110111101111001100110011101110000010101010000001111011001011110101011110101011011100001100000101001011101010000000100100000100100001010000101110101110110110110011000001101110100000001000010111111
00111010100111010100100000101001000000011011111110011010001000010010101011010011111000111001100100010001000011101001011101001011011010001000001000110110000011110111010001111010001110100011101010101010101101101110010111101100100111000001000010111111
00011111000011111001010101000010101011011101101101011100110001100111011100001110011101111001100110110110001100001110000001110000110110100000100001100100011001101111000000111000000111100011110000110000110010010110000001111110011011001001011001100011
01110100011110100011010000111110100000011101111110011101000110001101110110100101100110110111011011011000001110100011000100011000010010101000101001010001101011100110110010000110010000111110011010011010010000001000010001101101011111000001001001011010
10000000000000000000000000000000000000000000000000000001111111111111111110000000001111111111111111110000000001111111111111111110000000000000000000000000001111111110000000000000000001111111111111111111111111111111111111111111111100110111011000011110
mindist=118
weight enumerator=1 [0]  415 [118]  550 [120]  435 [122]  220 [124]  7 [128]  128 [134]  
122 [136]  100 [138]  42 [140]  1 [150]  8 [152]  9 [154]  10 [156]  

q=2 k=11 n=251 d=120
(extension of a code using automorphisms)
( link )

generator matrix:
00000000001111111110000000001111111110000000001111111110000000000111111110000111110000000001111111110000111110000000001111111110000001111111111110000011110001111110000000001111111110000001110000000000001111110000000110100000011111010010000100111011010
00001111110001111110000000110011111110000001110001111110000011111000011111111001110000011110000111110111000010001111110001111110001110000001111110001100010010011110000111110000111110001110110000001111110001110011111011100111101101100100000110010011101
00010000110010000110001111010100011110000111111110000110000100001000100010001000010001101110111000110001001110000001110000001110010010001110001110010111110100001110111000110111000110010010110011110011110110110101111011111001110100110000001010110101011
00110011110110011110110111101001101110111010110110111010000100001011101110111000010110100010001011010111010110000010010000010010110110110110110111111000110110110111001001011001001010110100010000010000011001001110001000000000101000000000110101110010100
00010101000010101000111011101001110111001111011011001110011000110011101111000010110000110111011000010011110110111110110111110110010010010010010011100101111011011011110011001110011000101110000111110111111011010000111011100010010011000000010011011111000
00011000000011000001011001111110110011010110000001010111100111001000100010001010111011110011001101111010101110000110110000110111001000101010101010001001001000011101011110011011110011110110100100010100011011011011001110000100101100000000111111000111111
00111000010111000011100111010111001110100111001000100110111101111001100110011101110000010101010000001111011001011110101011110101011011100001100000101001011101010000000100100000100100001010000101110101110110110110011000001101110100000001000011100011110
00111010100111010100100000101001000000011011111110011010001000010010101011010011111000111001100100010001000011101001011101001011011010001000001000110110000011110111010001111010001110100011101010101010101101101110010111101100100111000001000011100011110
00011111000011111001010101000010101011011101101101011100110001100111011100001110011101111001100110110110001100001110000001110000110110100000100001100100011001101111000000111000000111100011110000110000110010010110000001111110011011001001011111011100011
01110100011110100011010000111110100000011101111110011101000110001101110110100101100110110111011011011000001110100011000100011000010010101000101001010001101011100110110010000110010000111110011010011010010000001000010001101101011111000001001001010110101
10000000000000000000000000000000000000000000000000000001111111111111111110000000001111111111111111110000000001111111111111111110000000000000000000000000001111111110000000000000000001111111111111111111111111111111111111111111111100110111011111101000001
mindist=120
weight enumerator=1 [0]  813 [120]  773 [124]  41 [128]  222 [136]  166 [140]  4 [144]  5
 [152]  21 [156]  2 [160]  
This is a self-orthogonal code

q=2 k=11 n=257 d=122
(extension of a code using automorphisms)
( link )

generator matrix:
00000000001111111110000000001111111110000000001111111110000000000111111110000111110000000001111111110000111110000000001111111110000001111111111110000011110001111110000000001111111110000001110000000000001111110000000110100000011111010010000100111100001111101
00001111110001111110000000110011111110000001110001111110000011111000011111111001110000011110000111110111000010001111110001111110001110000001111110001100010010011110000111110000111110001110110000001111110001110011111011100111101101100100000110011010101000101
00010000110010000110001111010100011110000111111110000110000100001000100010001000010001101110111000110001001110000001110000001110010010001110001110010111110100001110111000110111000110010010110011110011110110110101111011111001110100110000001011100101011010100
00110011110110011110110111101001101110111010110110111010000100001011101110111000010110100010001011010111010110000010010000010010110110110110110111111000110110110111001001011001001010110100010000010000011001001110001000000000101000000000110010010101101010010
00010101000010101000111011101001110111001111011011001110011000110011101111000010110000110111011000010011110110111110110111110110010010010010010011100101111011011011110011001110011000101110000111110111111011010000111011100010010011000000010101010011100111011
00011000000011000001011001111110110011010110000001010111100111001000100010001010111011110011001101111010101110000110110000110111001000101010101010001001001000011101011110011011110011110110100100010100011011011011001110000100101100000000111001110000110000110
00111000010111000011100111010111001110100111001000100110111101111001100110011101110000010101010000001111011001011110101011110101011011100001100000101001011101010000000100100000100100001010000101110101110110110110011000001101110100000001000010111111000100010
00111010100111010100100000101001000000011011111110011010001000010010101011010011111000111001100100010001000011101001011101001011011010001000001000110110000011110111010001111010001110100011101010101010101101101110010111101100100111000001000010111111000100010
00011111000011111001010101000010101011011101101101011100110001100111011100001110011101111001100110110110001100001110000001110000110110100000100001100100011001101111000000111000000111100011110000110000110010010110000001111110011011001001011001100011000010010
01110100011110100011010000111110100000011101111110011101000110001101110110100101100110110111011011011000001110100011000100011000010010101000101001010001101011100110110010000110010000111110011010011010010000001000010001101101011111000001001001011010011110110
10000000000000000000000000000000000000000000000000000001111111111111111110000000001111111111111111110000000001111111111111111110000000000000000000000000001111111110000000000000000001111111111111111111111111111111111111111111111100110111011000011110101100010
mindist=122
weight enumerator=1 [0]  395 [122]  500 [124]  306 [126]  306 [128]  106 [130]  14 [132]  
114 [138]  118 [140]  70 [142]  72 [144]  18 [146]  3 [154]  6 [156]  8
 [158]  5 [160]  4 [162]  2 [164]  

ternary q=3

q=3 k=10 n=36 d=18 optimal
(extension of a code using automorphisms)
( link )

generator matrix:
001101110111111101111101110011000101
000210021222002210221210020011000111
012110111112020202221111211111001020
102201022021222100122101201212112202
200001202012212210222021011010121220
111221122002220210220101010120222112
002221220102100211221110000220102211
020212121200002110101122010101200200
222012110002200101222202212021101002
120022101010220102021211001211102101
mindist=18
weight enumerator=1 [0]  3840 [18]  11736 [21]  27000 [24]  13520 [27]  2952 [30]  
This is a self-orthogonal code

q=4

q=4 k=6 n=169 d=122 
(extension of a code using automorphisms)
( link )

generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:
[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]]
[[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:
[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:
[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:
[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,0]:[1,0]:[1,0]:
[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,0]:
[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:
[1,0]:[1,0]:[1,0]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:
[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:
[0,1]]
[[0,0]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:
[0,1]:[1,0]:[1,0]:[1,1]:[1,0]:[1,1]:[0,0]:[0,1]:[0,0]:[0,1]:[0,1]:[1,0]:
[0,1]:[1,1]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[1,1]:
[1,1]:[1,1]:[1,0]:[1,1]:[0,1]:[1,1]:[0,1]:[1,1]:[1,0]:[1,1]:[0,0]:[1,0]:
[0,1]:[0,1]:[0,0]:[0,1]:[1,0]:[1,1]:[1,0]:[1,0]:[1,0]:[1,1]:[0,0]:[1,1]:
[1,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,0]:[0,0]:
[1,0]:[1,1]:[0,0]:[0,0]:[0,1]:[1,1]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[1,1]:
[0,0]:[1,0]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:
[0,0]:[1,0]:[0,0]:[0,0]:[0,1]:[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:[0,0]:[1,0]:
[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:
[0,1]:[1,1]:[1,0]:[1,0]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:
[0,1]:[1,0]:[0,1]:[1,0]:[0,1]:[1,0]:[0,1]:[1,1]:[0,1]:[1,0]:[1,0]:[1,1]:
[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:
[1,0]:[0,0]:[0,0]:[1,1]:[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[1,1]:
[1,1]]
[[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:
[1,0]:[1,1]:[0,1]:[1,0]:[0,0]:[1,0]:[0,1]:[1,0]:[0,1]:[0,0]:[1,0]:[0,1]:
[0,1]:[1,1]:[1,1]:[1,0]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:
[0,1]:[1,1]:[1,0]:[1,0]:[1,1]:[0,1]:[1,1]:[1,0]:[1,1]:[0,1]:[1,0]:[1,0]:
[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[1,0]:[1,0]:[1,1]:[0,1]:
[0,0]:[1,0]:[0,1]:[0,0]:[1,1]:[0,1]:[1,1]:[0,0]:[1,0]:[0,0]:[1,0]:[1,1]:
[1,0]:[0,1]:[0,0]:[0,0]:[1,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,1]:[0,0]:
[1,0]:[0,1]:[1,1]:[1,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:
[1,0]:[0,0]:[0,1]:[1,1]:[0,0]:[0,0]:[0,1]:[1,1]:[0,0]:[0,1]:[1,0]:[0,0]:
[0,1]:[1,0]:[1,1]:[1,0]:[1,1]:[1,1]:[0,1]:[1,1]:[0,1]:[1,0]:[1,1]:[1,1]:
[1,0]:[1,0]:[0,1]:[1,1]:[0,1]:[1,0]:[1,0]:[0,0]:[1,0]:[0,1]:[1,1]:[0,0]:
[1,1]:[1,0]:[0,1]:[1,1]:[0,1]:[1,1]:[0,1]:[1,0]:[0,0]:[0,0]:[1,1]:[1,0]:
[0,1]:[1,1]:[1,0]:[0,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:
[0,0]:[0,0]:[1,0]:[0,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:[0,0]:[0,0]:
[0,1]]
[[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
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mindist=122
weight enumerator=1 [0]  630 [122]  696 [123]  198 [124]  288 [125]  828 [126]  552 [127
]  207 [128]  84 [129]  18 [130]  12 [131]  108 [133]  90 [134]  18 [135
]  108 [139]  42 [140]  162 [142]  54 [143]  

q=4 k=6 n=147 d=106
(computed using a programm of Johannes Zwanzger)
( link )
generator matrix:
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mindist=106
weight enumerator=1 [0]  756 [106]  495 [107]  750 [108]  414 [109]  558 [110]  234 [111
]  117 [112]  108 [113]  66 [114]  72 [115]  36 [116]  48 [117]  54 [118
]  18 [119]  6 [120]  54 [122]  93 [123]  162 [124]  54 [125]  

q=4 k=6 n=144 d=104
( using automorphisms)
( link )

code with group 36565 

generator matrix:
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]
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]
[[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[1,1]:
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]
[[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,0]:[0,1]:[1,0]:
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[1,0]:[1,1]:[0,1]:[1,1]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[0,1]:
[0,1]:[1,0]:[1,0]:[0,1]:[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[1,0]:[0,1]:
[1,0]:[0,1]:[0,1]:[1,0]:[1,0]:[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[0,1]:
[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,1]:[1,1]:[1,0]:[0,0]:[0,0]
]

corresponding to the solution:
[1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0
,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,0,0,0,0]
mindist=104
weight enumerator=1 [0]  1143 [104]  1224 [106]  768 [108]  288 [110]  135 [112]  96 [114
]  72 [116]  153 [120]  216 [122]  

q=4 k=6 n=138 d=99
( using automorphisms)
( link )

code with group 36565 

generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
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[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
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[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]]
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[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]]
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[0,0]:[0,0]:[1,0]:[1,1]:[0,1]:[1,1]]
[[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[1,1]:
[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,0]:[0,1]:[0,1]:
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[1,0]:[1,0]:[1,1]:[1,1]:[0,1]:[0,0]:[1,1]:[0,1]:[0,1]:[0,1]:[0,1]:[0,0]:
[1,1]:[1,0]:[1,0]:[0,0]:[1,1]:[1,0]:[1,1]:[1,0]:[0,1]:[0,0]:[0,1]:[0,0]:
[0,1]:[0,0]:[0,0]:[1,0]:[0,0]:[0,0]:[1,1]:[1,0]:[0,1]:[1,1]:[1,0]:[0,1]:
[1,1]:[1,0]:[1,1]:[0,1]:[1,1]:[1,1]:[1,0]:[1,1]:[0,1]:[1,1]:[1,0]:[1,1]:
[0,0]:[0,0]:[1,1]:[0,1]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,0]:[1,0]:[1,0]:
[0,1]:[0,1]:[1,0]:[0,1]:[0,0]:[0,0]:[0,1]:[1,1]:[0,0]:[1,1]:[1,0]:[0,0]:
[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]]
[[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,0]:[0,1]:[1,0]:
[0,1]:[0,1]:[1,0]:[0,0]:[1,0]:[0,0]:[1,1]:[1,0]:[1,1]:[1,1]:[0,1]:[0,0]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,0]:[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:[0,1]:[1,0]:
[0,1]:[1,1]:[1,0]:[1,1]:[0,1]:[1,0]:[1,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,1]:
[1,0]:[1,1]:[0,1]:[1,1]:[1,0]:[1,0]:[0,1]:[0,0]:[1,1]:[1,0]:[0,1]:[0,0]:
[1,0]:[1,0]:[0,1]:[0,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,1]:[0,1]:[1,1]:[0,1]:
[0,0]:[1,1]:[1,0]:[1,1]:[0,0]:[1,0]:[1,0]:[1,1]:[0,0]:[1,1]:[0,0]:[0,1]:
[0,0]:[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[1,0]:[1,1]:[0,1]:[1,1]:[0,1]:[1,0]:
[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[0,1]:[0,1]:[1,0]:[1,0]:[0,1]:[0,0]:[0,0]:
[0,1]:[1,0]:[0,0]:[0,0]:[1,0]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[1,0]:[0,0]:
[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[0,1]:[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:
[0,1]:[1,1]:[1,1]:[1,0]:[0,0]:[0,0]]

corresponding to the solution:
[1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0
,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,0,0,0,0]
mindist=99
weight enumerator=1 [0]  468 [99]  621 [100]  540 [101]  756 [102]  432 [103]  378 [104]  
144 [105]  90 [106]  36 [107]  87 [108]  36 [109]  72 [110]  48 [111]  
18 [112]  6 [114]  72 [115]  108 [116]  144 [117]  36 [118]  3 [120]  

q=4 k=7 n=94 d=64
( using automorphisms)
( link )

code with group 36681 

generator matrix:
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[1,1]:[1,1]:[1,0]:[0,1]:[0,1]:[1,1]:[1,0]:[1,0]:[0,1]:[1,1]]

corresponding to the solution:
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,0,0,0,0,0,0,0]
mindist=64
weight enumerator=1 [0]  2613 [64]  4860 [68]  5328 [72]  3204 [76]  378 [80]  

q=4 k=7 n=110 d=76
( using automorphisms)
( link )

code with group 35248 

generator matrix:
[[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
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[1,1]:[0,0]]
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corresponding to the solution:
[0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=76
weight enumerator=1 [0]  3150 [76]  4338 [80]  5100 [84]  3120 [88]  630 [92]  45 [96]  

q=4 k=7 n=159 d=112
(computed using a programm of Johannes Zwanzger)
( link )
generator matrix:
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mindist=112
weight enumerator=1 [0]  3633 [112]  3168 [116]  4935 [120]  2244 [124]  2076 [128]  324
 [132]  3 [152]  

q=4 k=7 n=203 d=144
(computed using a programm of Johannes Zwanzger)
( link )
generator matrix:
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mindist=144
weight enumerator=1 [0]  2565 [144]  4173 [148]  3642 [152]  3279 [156]  1440 [160]  945
 [164]  336 [168]  3 [188]  

q=4 k=7 n=208 d=148
(computed using a programm of Johannes Zwanzger)
( link )
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mindist=148
weight enumerator=1 [0]  2934 [148]  4245 [152]  3465 [156]  2760 [160]  1800 [164]  945
 [168]  225 [172]  3 [176]  6 [184]  

q=4 k=7 n=214 d=152
( using automorphisms)
( link )

code with group 79416 

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corresponding to the solution:
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,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0]
mindist=152
weight enumerator=1 [0]  2583 [152]  3855 [156]  3825 [160]  2898 [164]  1914 [168]  855
 [172]  450 [176]  3 [184]  

q=4 k=9 n=117 d=75
( using automorphisms)
( link )

code with group 127116 

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[1,0]:[1,0]:[1,0]:[1,1]:[0,0]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:
[1,1]:[0,0]:[1,0]:[1,0]:[0,1]:[0,1]:[1,1]:[1,1]:[1,1]]
[[0,0]:[0,0]:[0,1]:[0,0]:[0,0]:[1,0]:[1,1]:[0,1]:[1,1]:[0,0]:[1,1]:[1,0]:
[1,1]:[1,1]:[0,1]:[0,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,1]:[0,1]:[1,0]:[1,1]:
[0,1]:[0,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,1]:[0,0]:[1,0]:[1,1]:[0,0]:[1,1]:
[0,0]:[1,1]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[0,0]:[0,1]:[1,0]:
[1,1]:[0,1]:[1,0]:[0,0]:[1,0]:[1,1]:[1,1]:[1,0]:[1,1]:[1,0]:[0,0]:[0,0]:
[0,1]:[0,1]:[1,1]:[0,0]:[0,0]:[1,0]:[1,0]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]:
[0,1]:[0,1]:[1,0]:[1,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,0]:[1,1]:[0,0]:
[1,0]:[1,0]:[0,1]:[0,1]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:[0,1]:[0,1]:
[0,0]:[0,1]:[1,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,1]:
[0,0]:[0,1]:[1,0]:[1,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]]
[[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[1,1]:[1,0]:[1,0]:[0,1]:[0,0]:[0,1]:[1,1]:
[0,1]:[1,1]:[1,0]:[0,1]:[1,1]:[1,1]:[1,0]:[1,0]:[0,1]:[1,1]:[1,1]:[0,0]:
[1,1]:[1,1]:[1,1]:[0,1]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[1,0]:[1,1]:[1,1]:
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[0,1]:[1,1]:[1,1]:[0,1]:[0,0]:[0,1]:[0,0]:[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:
[1,0]:[1,1]:[0,1]:[0,0]:[1,1]:[0,0]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[0,1]:
[0,1]:[1,1]:[0,1]:[0,1]:[0,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,0]:[1,0]:[1,0]:
[0,1]:[1,1]:[0,0]:[1,0]:[0,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,0]:[1,0]:
[0,1]:[0,1]:[0,0]:[1,0]:[1,0]:[0,0]:[0,0]:[0,1]:[1,0]:[1,0]:[0,1]:[0,1]:
[0,1]:[1,0]:[0,0]:[0,1]:[0,1]:[0,0]:[1,1]:[1,0]:[0,0]]
[[0,0]:[1,1]:[1,1]:[0,1]:[1,0]:[1,1]:[1,1]:[0,0]:[1,0]:[1,1]:[0,0]:[0,1]:
[0,0]:[1,0]:[0,1]:[1,1]:[0,1]:[1,1]:[1,0]:[1,0]:[0,1]:[1,0]:[0,1]:[1,0]:
[1,0]:[0,1]:[0,0]:[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,1]:[1,1]:[0,1]:[0,0]:
[1,0]:[0,0]:[1,1]:[0,0]:[0,1]:[0,0]:[1,1]:[0,1]:[1,0]:[0,0]:[0,0]:[0,1]:
[1,1]:[0,0]:[0,0]:[0,0]:[1,0]:[1,1]:[1,0]:[0,1]:[0,0]:[1,0]:[1,0]:[0,0]:
[0,1]:[1,0]:[1,0]:[1,1]:[1,0]:[1,0]:[1,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:
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[0,1]:[0,0]:[0,1]:[1,1]:[1,0]:[1,1]:[0,1]:[1,0]:[1,0]:[1,1]:[1,0]:[1,0]:
[1,0]:[1,0]:[0,0]:[1,0]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,0]:[0,0]:
[0,0]:[1,0]:[1,1]:[0,1]:[0,0]:[0,0]:[1,0]:[1,0]:[1,0]]
[[0,0]:[0,1]:[0,0]:[1,1]:[1,1]:[1,1]:[0,1]:[1,0]:[0,0]:[0,1]:[1,0]:[1,0]:
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[1,1]:[1,1]:[0,1]:[0,0]:[0,0]:[1,1]:[0,1]:[1,0]:[0,1]:[0,1]:[1,0]:[0,0]:
[0,0]:[1,0]:[1,0]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:[1,0]:[1,1]:[1,1]:[0,1]:
[1,1]:[1,1]:[1,0]:[1,1]:[1,1]:[1,0]:[0,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,1]:
[0,1]:[1,1]:[0,0]:[0,1]:[0,0]:[1,0]:[1,0]:[0,0]:[0,1]:[1,1]:[1,1]:[1,0]:
[1,0]:[0,0]:[0,1]:[1,1]:[0,0]:[1,0]:[0,0]:[1,0]:[1,1]:[1,1]:[1,0]:[0,1]:
[1,0]:[1,1]:[0,0]:[0,0]:[1,1]:[0,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:
[1,1]:[1,1]:[0,1]:[0,0]:[0,0]:[0,1]:[0,0]:[1,1]:[1,1]:[0,0]:[1,0]:[0,0]:
[1,0]:[0,0]:[0,0]:[1,1]:[0,1]:[0,0]:[1,1]:[1,0]:[0,0]]
[[0,0]:[1,0]:[0,1]:[1,0]:[1,0]:[0,1]:[0,0]:[1,0]:[1,1]:[1,0]:[1,1]:[0,1]:
[1,0]:[1,0]:[0,1]:[1,0]:[1,0]:[1,1]:[1,0]:[1,1]:[1,0]:[0,0]:[0,0]:[1,0]:
[1,0]:[0,1]:[1,0]:[1,1]:[0,0]:[1,0]:[0,1]:[1,0]:[0,1]:[1,0]:[1,1]:[1,1]:
[0,0]:[0,0]:[0,0]:[1,0]:[0,1]:[1,0]:[0,0]:[0,0]:[0,1]:[1,1]:[1,1]:[0,0]:
[1,0]:[0,1]:[0,0]:[0,1]:[1,1]:[0,1]:[1,1]:[0,1]:[1,1]:[1,1]:[1,0]:[0,0]:
[0,0]:[1,1]:[0,0]:[1,0]:[1,1]:[0,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,0]:[1,1]:
[1,0]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[1,0]:[1,0]:
[1,0]:[1,1]:[1,0]:[1,1]:[0,1]:[0,1]:[1,0]:[0,1]:[0,0]:[1,0]:[0,1]:[0,1]:
[1,1]:[1,1]:[0,0]:[1,0]:[0,0]:[0,0]:[0,1]:[1,1]:[1,1]:[1,1]:[1,0]:[0,0]:
[0,1]:[1,1]:[1,1]:[0,0]:[1,0]:[0,1]:[0,0]:[1,1]:[1,0]]
[[0,0]:[0,1]:[0,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,0]:[1,0]:[1,1]:[0,1]:[0,0]:
[1,0]:[0,0]:[0,1]:[1,1]:[0,0]:[0,0]:[1,0]:[0,1]:[1,0]:[0,1]:[1,1]:[0,1]:
[0,0]:[1,1]:[0,0]:[1,0]:[1,1]:[0,1]:[0,0]:[0,1]:[1,1]:[0,1]:[1,1]:[1,0]:
[0,0]:[0,1]:[1,1]:[0,1]:[0,0]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,0]:
[0,0]:[1,1]:[1,0]:[1,1]:[0,1]:[0,0]:[1,1]:[0,1]:[1,0]:[0,1]:[0,0]:[1,1]:
[0,1]:[1,1]:[0,1]:[1,1]:[1,0]:[0,1]:[1,0]:[1,0]:[1,0]:[0,0]:[0,0]:[1,0]:
[1,1]:[0,0]:[0,1]:[0,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,0]:[1,0]:[0,0]:[1,1]:
[1,0]:[0,1]:[1,1]:[0,1]:[1,1]:[1,1]:[1,1]:[0,1]:[1,1]:[0,1]:[0,1]:[0,0]:
[0,0]:[0,0]:[1,0]:[1,1]:[0,1]:[0,1]:[1,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,0]:[0,0]:[0,1]:[0,0]:[1,0]:[0,1]:[1,1]:[0,0]]
[[1,1]:[0,0]:[1,1]:[1,1]:[0,0]:[1,0]:[0,1]:[1,0]:[1,0]:[1,0]:[0,0]:[0,1]:
[0,1]:[0,0]:[1,1]:[1,0]:[0,1]:[0,0]:[0,0]:[0,0]:[1,1]:[1,0]:[0,1]:[1,0]:
[0,0]:[1,0]:[0,0]:[0,1]:[1,0]:[0,0]:[1,1]:[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:
[0,1]:[0,0]:[1,0]:[1,0]:[0,0]:[1,1]:[1,0]:[1,0]:[0,1]:[1,1]:[0,1]:[1,1]:
[1,0]:[0,0]:[1,0]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,0]:[0,0]:[1,0]:[1,0]:
[1,0]:[0,1]:[1,1]:[1,1]:[1,0]:[1,0]:[0,0]:[1,1]:[1,1]:[0,1]:[0,0]:[1,0]:
[1,0]:[1,0]:[1,1]:[1,0]:[0,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[1,1]:
[1,0]:[0,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,0]:[1,1]:[1,1]:[1,0]:[1,0]:[1,1]:
[0,1]:[0,0]:[1,1]:[0,0]:[0,1]:[1,1]:[0,1]:[0,1]:[0,0]:[0,0]:[0,0]:[0,1]:
[1,0]:[1,0]:[0,1]:[1,0]:[1,0]:[0,1]:[0,0]:[1,1]:[1,0]]
corresponding to the solution:
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,0,0,1,1,0,1,0]
mindist=75
weight enumerator=1 [0]  630 [75]  1470 [76]  1929 [77]  3888 [78]  4779 [79]  5670 [80]  
7146 [81]  9882 [82]  12096 [83]  15321 [84]  17961 [85]  20073 [86]  22305
 [87]  23058 [88]  21312 [89]  20016 [90]  18342 [91]  15075 [92]  12771
 [93]  9837 [94]  6831 [95]  4833 [96]  2943 [97]  1836 [98]  1080 [99
]  540 [100]  351 [101]  84 [102]  81 [103]  3 [113]  

q=5

q=7

q=8

q=9