length n = 123
dimension k = 7
alphabet length q = 3

minimum distance d = 75

generator matrix:
000000000110000000000000000111111111111111111111111000000000000000011111111111111111111111111111111111111111111111111111111
000000011000000000011111111000000001111111122222222111111111111111100000000000000001111222211111111222222221111111122222222
000001100001111111100000000111122220000112200001122111111112222222200000000111122220000000011112222111122221111222211112222
000110000001111222211112222112211220000000000000000000011220000112211112222000000001122112211221122112211221122112211221122
011000000001122112211221122000000001122000011220000112200001122000011221122112211220000000012121212121212121212121212121212
112121212120000000000000000000000000000000000000000121212121212121212121212121212121212121212212112211212212112122112212112
012121212121212121212121212121212121212121212121212000000000000000000000000000000000000000021121221122121121221211221121221

projective group of automorphisms generated by:
0000100
0001000
0100000
1000000
0010000
0000010
0000001

0001000
0000100
0010000
1000000
0100000
0000010
0000001

2000000
0100000
0010000
0001000
0000200
0000010
0000001