The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+57x^76+48x^77+93x^78+138x^79+158x^80+232x^81+225x^82+206x^83+203x^84+210x^85+234x^86+230x^87+235x^88+220x^89+197x^90+212x^91+199x^92+172x^93+135x^94+142x^95+93x^96+104x^97+75x^98+78x^99+57x^100+34x^101+40x^102+18x^103+15x^104+4x^105+19x^106+4x^108+2x^110+2x^112+4x^114

The gray image is a linear code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 3.93 seconds.