The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  0  1  1  1  X  1  1  0  1  0  1  1  0  1  0  1  X  1  1  1  1  1  1  1  0  X  1  0  X  1  X  1  1  1  1  1  1  1  0  0  1  1  0  1  1  1  1  1  X  1  1  1  1  1  0  0  X  1  0  1  1  0  1  0  1  1  0  1  X  0  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  X X+1  1  0  1 X+1  X X+1  1 X+1  0  1  X  1 X+1  0  1 X+1  1  1  1  0 X+1  0 X+1  1  X  1  1  1  0  1  1  X  1  1  1  0  X  1 X+1 X+1  1  1  X  1  1 X+1  X X+1  0  X  1  0 X+1 X+1 X+1  1  1  1  1  X  1 X+1 X+1  1  0  1 X+1 X+1  1  1  1  1 X+1  1
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  X  X  X  X  0  X  0  0  X  X  X  X  X  0  X  0  0  0  X  0  0  0  X  X  X  0  0  X  0  0  0  0  X  X  0  0  0  X  X  X  0  0  X  X  0  0  X  X  X  0  0  0  0  0  X  X  0  X  X  X  X  0  0  X  0  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  X  0  0  0  0  X  X  X  0  X  0  X  0  X  X  0  X  X  X  0  0  0  0  X  0  X  X  X  0  X  0  X  X  X  0  0  X  X  0  0  X  0  X  0  X  X  0  X  X  0  X  X  0  X  X  X  0  0  X  X  X  0  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  0  0  X  X  X  0  0  0  0  X  X  X  0  0  X  X  X  0  X  0  X  0  X  0  X  X  0  X  0  X  X  X  X  X  0  0  X  0  X  X  0  0  0  X  0  0  0  0  0  X  0  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  0  X  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  X  0  X  X  0  0  X  X  0  X  X  X  X  X  0  X  0  0  0  0  0  X  0  X  X  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  X  X  X  0  X  0  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0  0  X  0  X  0  0  X  X  0  0  X  0  X  0  X  0  X  0  X  X  0  0  X  0  X  X  0  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  X  X  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  X  X  0  0  X  X  X  X  X  X  0  0  X  X  0  X  0  0  X  0  0  0  0  X  0  X  0  0  X  X  0  0  0  X  X  X  0  X  0  X  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  0  X  0  0  0  X  X  X  0  0  X  0  X  X  0  X  X  0  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  0  X  X  0  X  0  0  0  X  0  0  X  X  X  X  0  X  0  X  X  X  X  0  0  X  0  X  X  0  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  0  0  0  X  X  0  0  0  X  0  0  X  X  0  0  0  X  X  X  X  0  0  X  X  0  X  0  0  X  X  0  0  X  0  0  X  X  0  0  0  X  X  X  X  X  0  0  X  X  0  X  X  0  X  X  0  X  X  0  X  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+148x^76+94x^78+413x^80+294x^82+518x^84+380x^86+500x^88+380x^90+482x^92+294x^94+310x^96+94x^98+100x^100+48x^104+30x^108+7x^112+2x^116+1x^128

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 4.94 seconds.