The generator matrix
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 X 1 1 1 1 1 X 1 1 1 1 X 1 X 1 1 1 1 X 1 X 1 1 X 1 0 1 1 1 X 1 1 1 1 X X X
0 X 0 0 0 0 0 0 0 0 X 0 X X 0 X X 0 0 X X 0 0 0 0 0 0 X 0 X X 0 0 X X X 0 X 0 X X X 0 0 X X X X 0 X X X 0 0 0 0 0 X X X X 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X X 0 0 0 0 X X 0 X
0 0 X 0 0 0 0 0 0 0 X X X 0 X X 0 0 X X 0 0 0 X 0 0 0 0 X X X X X X 0 X 0 0 0 0 0 0 X X X X X X X 0 0 X X 0 0 0 X X 0 X 0 X X X 0 X X 0 0 X X X X 0 0 0 0 X 0 0 0 0 X 0 X 0
0 0 0 X 0 0 0 0 0 X 0 X 0 X X 0 X 0 X X X X X 0 0 X X X 0 0 X X 0 X X X X X X X X X X 0 X 0 0 X 0 0 X X X X 0 X 0 X 0 X 0 X 0 0 0 X 0 X 0 0 0 X X X X X X 0 X 0 X 0 0 0 X X
0 0 0 0 X 0 0 0 0 X 0 0 0 0 X X X 0 0 0 0 X X X 0 X 0 X 0 X X X X 0 0 X 0 X 0 X 0 0 X 0 0 0 0 X X X X X 0 0 0 X 0 0 X 0 0 0 X 0 X X 0 X X X 0 0 X X 0 0 0 X X X X 0 0 0 0 X
0 0 0 0 0 X 0 0 0 X 0 0 X X X X 0 X X 0 X 0 0 0 0 X 0 0 X 0 0 0 X X X X X X X X X X X 0 0 0 X 0 0 X 0 0 X 0 X X X 0 0 X 0 0 0 0 0 0 X 0 X X 0 0 X 0 X X 0 0 0 0 X X X X X 0
0 0 0 0 0 0 X 0 0 X 0 X X 0 0 0 0 0 0 0 X X X X X X 0 0 X X 0 X 0 X 0 X X 0 0 X X X X X 0 X 0 0 X X X X X X X X X X X 0 0 0 0 X 0 X X 0 0 X 0 0 X 0 X 0 0 X 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 X 0 X X X 0 0 0 X X X X 0 X X 0 X X X X 0 X 0 X X X X X 0 X 0 X X 0 0 0 0 X X X 0 X X X X X 0 0 X 0 X X 0 X X X X X X 0 X 0 X X 0 X X X X 0 X 0 X 0 X X 0 X 0
0 0 0 0 0 0 0 0 X X X 0 0 X 0 0 0 0 X 0 0 X X X X 0 X X 0 0 0 X X X 0 0 X X 0 X 0 X 0 0 0 0 X 0 0 X X X 0 0 X 0 X 0 0 X X 0 0 X X 0 0 0 X 0 X 0 0 X X X X 0 X X 0 X 0 0 0 X
generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.
Homogenous weight enumerator: w(x)=1x^0+88x^76+6x^78+137x^80+68x^82+193x^84+112x^86+164x^88+60x^90+84x^92+10x^94+53x^96+30x^100+12x^104+4x^108+1x^112+1x^148
The gray image is a linear code over GF(2) with n=172, k=10 and d=76.
This code was found by Heurico 1.16 in 0.462 seconds.