The generator matrix

1 0 0 0 0 0 1 1 1 1 0 0 X 1 1 1 1 1 1 1 1 X 1 1 1 0 X 0 X X 0 0 1 X X 0 X X 1 1 1 X 1 1 1 0 1 X 1 0 X 1 0 X X 1 0 X 1 0 1 1 1 X 1 1 X 1 X 1 1 X X 1 0 1 1 1 1 0 1 1 0 1 0 X 1
0 1 0 0 0 0 0 0 0 0 0 X X X 0 0 0 X 0 X X X X X 0 X 0 0 0 0 0 1 1 1 1 1 1 1 1 X+1 X+1 1 X+1 1 1 1 1 1 X+1 1 X X+1 1 1 1 1 1 1 X+1 1 X X+1 X+1 1 1 0 X X+1 0 X X 1 0 X+1 0 X+1 X 1 X 1 X+1 1 0 X 1 X 0
0 0 1 0 0 0 0 0 0 X X X X 0 0 1 1 1 X+1 1 1 1 X+1 0 1 1 1 1 1 1 1 X X X+1 1 X X+1 1 X 0 0 X 0 0 1 X+1 X+1 0 X+1 X 1 X 0 X 0 1 1 1 0 X+1 0 X+1 1 X X X+1 0 X 1 X 0 X X 1 1 X+1 0 0 1 1 1 0 X X+1 X+1 0 0
0 0 0 1 0 0 0 1 X 1 1 1 X X+1 X+1 1 X+1 0 X+1 X 0 1 X X X+1 X X+1 X+1 X 1 X 1 X 0 X 0 X+1 0 0 0 1 X+1 0 1 0 0 1 X+1 X+1 X X X+1 X+1 X+1 1 X+1 X+1 X+1 1 0 0 X X+1 1 0 1 X 0 X 0 1 X 1 0 X 1 1 X 1 X+1 X+1 X 1 1 1 0 1
0 0 0 0 1 0 1 X 0 1 X 1 1 1 X X 0 1 X+1 0 X+1 0 0 X+1 X+1 1 1 X+1 X X 1 X+1 X X X 1 X+1 X+1 X+1 0 X X 1 0 0 1 X 1 1 X 1 X+1 X+1 0 0 X+1 1 X X+1 X X+1 0 1 0 X+1 1 X X X+1 0 X+1 X 1 0 0 0 1 1 X+1 X 1 0 0 X X 1 0
0 0 0 0 0 1 X 0 1 1 X+1 X+1 X+1 0 X+1 X X+1 1 1 0 X 1 1 X+1 X X+1 0 1 1 0 0 X X 0 X+1 1 X+1 1 0 X+1 1 X 1 X 1 X 0 X+1 X 1 0 1 X X+1 0 X+1 X+1 0 0 0 0 X 0 X+1 X+1 1 1 X 1 X+1 X 0 X+1 0 X+1 0 1 0 1 X X+1 1 1 X X+1 1 0

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+49x^76+98x^77+171x^78+212x^79+171x^80+234x^81+271x^82+232x^83+202x^84+226x^85+198x^86+222x^87+234x^88+198x^89+207x^90+148x^91+145x^92+138x^93+118x^94+116x^95+128x^96+80x^97+66x^98+84x^99+48x^100+40x^101+25x^102+10x^103+14x^104+8x^105+2x^109

The gray image is a linear code over GF(2) with n=174, k=12 and d=76.
This code was found by Heurico 1.10 in 1.14 seconds.