The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 1 0 1 0 1 1 X 0 1 1 1 0 X 1 1 0 1 1 X X 0 1 1 0 X 1 0 X 1 1 0 1 X 1 0 1 0 1 1 1 0 X 1 1 1 0 0 1 X 1 1 X X 1 1 1 1 1 1 1 1 X 1
0 1 0 1 0 1 1 0 0 1 X+1 1 1 X 0 X 0 X+1 X+1 1 1 1 X X+1 X 1 X X 0 0 X 1 1 0 X 0 0 1 X+1 1 1 X+1 1 1 X+1 1 1 1 1 X X+1 X+1 0 1 1 X+1 1 X+1 1 1 X 1 X+1 0 X 1 1 1 1 0 1 X X+1 X 0 0
0 0 1 1 1 0 1 0 1 X+1 X X 1 0 1 1 1 X+1 0 1 0 1 1 0 1 0 1 X 1 X+1 1 0 1 1 X X 1 0 1 X+1 1 X+1 X 1 1 X X+1 0 X 1 1 X+1 1 X+1 0 0 X+1 0 1 X+1 X 0 X X+1 1 X+1 X+1 X+1 0 1 1 1 1 X 0 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X X X X X X 0 0 X X 0 0 X 0 0 X X 0 X 0 X 0 0 X X 0 X X 0 X X 0 X 0 0 X X 0 0 X X 0 0 X X X X 0 0 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 X X X X 0 0 X 0 X X X X X 0 X 0 0 X X 0 X 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 X X 0 X 0 0 0 0 0 X X X X 0 0 X 0 0 0 X X X 0 0 X X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X 0 0 X X X X X X X X X 0 0 X X 0 0 0 0 X X X X 0 X X X 0 0 X X X 0 0 0 0 X X 0 X 0 0 0 0 0 0 X X X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X X 0 X X X X 0 0 X 0 0 0 X 0 0 X 0 0 X X X 0 0 0 X 0 X X X X 0 0 X X X X 0 0 0 0 0 0 X X X 0 X 0 X 0 X X X X 0
0 0 0 0 0 0 0 X 0 X X 0 0 0 X X X X X 0 0 X 0 0 0 X X 0 X X X 0 0 0 0 0 0 X X X 0 0 X 0 X X 0 0 0 X 0 X 0 0 X 0 X X 0 0 X X X X X X X X 0 X X X 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 X 0 X X 0 X 0 X X 0 X X X X X X X X X 0 0 0 0 0 X 0 0 0 0 X 0 X 0 X X X 0 0 0 0 0 0 0 X 0 X 0 X X X 0 X X
generates a code of length 76 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+40x^64+52x^65+84x^66+134x^67+173x^68+166x^69+189x^70+220x^71+190x^72+218x^73+262x^74+248x^75+250x^76+266x^77+217x^78+224x^79+223x^80+168x^81+154x^82+142x^83+87x^84+122x^85+80x^86+52x^87+36x^88+26x^89+27x^90+4x^91+16x^92+6x^93+9x^94+6x^96+2x^100+1x^102+1x^106
The gray image is a linear code over GF(2) with n=152, k=12 and d=64.
This code was found by Heurico 1.16 in 3.26 seconds.