The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+82x^86+46x^88+62x^90+43x^92+14x^94+4x^96+1x^100+2x^114+1x^120

The gray image is a linear code over GF(2) with n=178, k=8 and d=86.
This code was found by Heurico 1.16 in 1.07 seconds.