The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  X  0  X  1  0  X  1  1  1  X  X  X  X  1  1  1  1  X  1  0  X  1  1  1  1  1  1  0  0  0  X  1  0  1  1  1  X  0  1  1  1  X  X  0  0  X  1  X  X  1  X  1  1  0  0  1  X  0  1  X  X  1  1  1  1  1  1  1  0  X  0
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  X  0  0  0  1  1  0  1  1  1  1  X  0  0  1  1  X  0  X X+1  1  X  0  1  0  0  X  X  1  1  0  1  0  X  X  1  1 X+1 X+1  1  1  0  0 X+1  1  1  0  X  X  X  1  1 X+1  0 X+1 X+1  X  1  1  0  1  X  1  X  0  X  1 X+1  X  0 X+1  1  1  1
 0  0  1  0  1  1  0  1  0  1  1  X  0  1  1  X  1  X  X  1  1  X  1  0 X+1  0  1  0  X X+1  1  X  1  1  X  0  1  0 X+1  0  X  0  0 X+1  1  0  1  X  0  X  1  X  X  X  1  0  0 X+1  1  1  1  0  1 X+1  X  1  X  1  0  0  1  X  0  1  1  X X+1  0 X+1 X+1  X  X  1  X  0  0  1 X+1
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  X  1 X+1  0  1  0  X  0 X+1  1  X  X  0  1  1  1  1  X X+1  0  1  X X+1  X  X  1  0  X  0  1 X+1 X+1 X+1  X  1  1 X+1  X  0 X+1  1  1  X  X X+1  0 X+1 X+1  1  X  1  0  1 X+1  0 X+1  0 X+1  1 X+1  1  X X+1  X  1 X+1  0  1 X+1  X  1  X X+1  1  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  X  0  0  X  X  0  X  0  X  0  X  X  0  X  0  X  X  X  0  0  X  0  0  0  X  0  X  X  X  0  0  0  X  X  0  X  0  X  X  0  X  X  X  0  X  X  0  X  X  0  0  X  0  X  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  X  0  X  0  X  0  0  0  X  X  0  0  0  X  X  0  X  X  X  X  X  X  0  X  0  0  X  X  0  X  X  X  0  X  0  X  0  0  0  0  0  0  0  0  0  X  X  0  0  X  X  X  X  X  X  X  0  0  X  X  0  X  X  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  0  X  X  0  X  0  X  0  0  X  0  X  0  X  X  0  X  X  X  X  0  0  X  0  X  0  X  X  X  X  0  0  0  X  X  0  0  0  X  0  0  0  0  X  X  X  0  X  X  0  X  0  X  0  0  0  0  X  0  0  X  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  X  X  0  0  0  X  0  0  0  0  X  X  0  X  0  0  X  0  X  0  X  X  X  0  X  0  0  0  X  0  X  0  X  X  X  X  X  X  X  0  X  X  X  0  0  X  0  X  X  0  X  X  X  X  0  X
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  X  X  X  0  X  X  X  0  X  0  X  0  0  0  X  0  X  X  X  X  X  0  X  X  0  0  0  X  X  0  X  X  X  X  X  X  X  0  X  X  X  X  0  0  X  0  0  0  0  X  X  X  X  0  X  0  0  0  0  0  0  0  X  X  0  X  X  0  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+243x^76+430x^78+688x^80+750x^82+800x^84+816x^86+902x^88+810x^90+820x^92+606x^94+574x^96+338x^98+233x^100+84x^102+72x^104+6x^106+15x^108+3x^112+1x^116

The gray image is a linear code over GF(2) with n=176, k=13 and d=76.
This code was found by Heurico 1.16 in 16.8 seconds.