The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+173x^76+262x^78+606x^80+536x^82+900x^84+776x^86+970x^88+800x^90+908x^92+696x^94+589x^96+384x^98+316x^100+120x^102+98x^104+8x^106+35x^108+2x^110+8x^112+4x^116

The gray image is a linear code over GF(2) with n=178, k=13 and d=76.
This code was found by Heurico 1.16 in 16.5 seconds.