length n = 126
dimension k = 4
alphabet length q = 8
minimum distance d = 108
generator matrix:
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | 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 | 1 | 1 | 0 | 0 | 1 | 2 | 2 | 3 | 3 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 4 | 4 | 5 | 5 | 5 | 6 | 6 | 7 | 7 | 7 | 7 | 1 | 0 | 0 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 5 | 6 | 6 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 4 | 4 | 4 | 6 | 6 | 7 | 7 | 7 | 7 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 3 | 3 | 4 | 6 | 6 | 6 | 6 | 7 | 7 | 7 | 7 | 0 | 0 | 2 | 2 | 3 | 3 | 6 | 6 | 7 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 7 |
| 1 | 1 | 2 | 3 | 5 | 6 | 0 | 4 | 7 | 0 | 1 | 2 | 4 | 7 | 5 | 5 | 1 | 5 | 0 | 0 | 3 | 3 | 7 | 1 | 6 | 2 | 6 | 0 | 0 | 4 | 3 | 7 | 1 | 2 | 4 | 5 | 1 | 2 | 3 | 6 | 7 | 3 | 6 | 6 | 7 | 2 | 2 | 3 | 5 | 4 | 6 | 3 | 2 | 4 | 2 | 4 | 3 | 0 | 3 | 3 | 6 | 1 | 1 | 0 | 1 | 3 | 5 | 5 | 6 | 2 | 2 | 0 | 1 | 7 | 0 | 1 | 4 | 4 | 0 | 0 | 2 | 6 | 7 | 7 | 1 | 6 | 0 | 1 | 2 | 4 | 2 | 3 | 6 | 7 | 6 | 0 | 4 | 3 | 7 | 1 | 1 | 2 | 4 | 6 | 0 | 2 | 3 | 3 | 6 | 7 | 4 | 6 | 2 | 4 | 3 | 7 | 2 | 0 | 1 | 3 | 7 | 0 | 7 | 1 | 4 | 4 |
| 2 | 6 | 1 | 5 | 7 | 2 | 4 | 6 | 2 | 7 | 0 | 0 | 7 | 4 | 4 | 6 | 2 | 2 | 1 | 7 | 4 | 2 | 6 | 7 | 0 | 4 | 2 | 6 | 7 | 0 | 2 | 4 | 0 | 0 | 6 | 6 | 5 | 0 | 4 | 7 | 3 | 7 | 2 | 4 | 0 | 1 | 3 | 7 | 6 | 4 | 6 | 4 | 7 | 1 | 4 | 5 | 7 | 0 | 4 | 7 | 1 | 2 | 3 | 4 | 7 | 4 | 2 | 7 | 0 | 4 | 6 | 6 | 3 | 7 | 7 | 4 | 3 | 6 | 0 | 1 | 6 | 1 | 0 | 4 | 0 | 6 | 3 | 1 | 3 | 1 | 7 | 0 | 1 | 4 | 4 | 7 | 4 | 6 | 3 | 0 | 3 | 1 | 6 | 7 | 0 | 6 | 0 | 6 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
projective group of automorphisms generated by: