length n = 7
dimension k = 6
alphabet length q = 4

minimum distance d = 2

generator matrix:
1111111
1111123
1111213
1112113
1121113
1211113

projective group of automorphisms generated by:
000001
100000
010000
001000
000100
000010

010000
100000
001000
000100
000010
000001