The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  0  1  1 X+1  0  1  0 X+1  1  0 X+1  1  0  1  1  0 X+1  1  0  1  1  X X+1  1  X X+1  1  X X+1  1  X X+1  1  X  1  1  X  1  1  X  1  1  X  1  1  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X X+1 X+1 X+1 X+1 X+1  1 X+1  1 X+1  1  1  1 X+1  1  1  1  0  0  0  X  0  X  0  0  X
 0  0  X  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  0  X  0  X  X  0  X  X  0  X  0  X  0  0  X  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  0  0  0  0  0  0  X  X  X  X  X
 0  0  0  X  0  X  X  X  X  0  X  0  0  0  X  X  X  0  X  0  0  0  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  0  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  X  0  0
 0  0  0  0  X  0  X  X  X  X  0  X  X  0  X  0  X  0  X  X  X  0  0  0  0  X  0  X  0  X  0  X  0  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  0  X  X  0  0  0  X  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+12x^86+18x^88+64x^89+18x^90+12x^92+1x^96+1x^114+1x^146

The gray image is a linear code over GF(2) with n=178, k=7 and d=86.
This code was found by Heurico 1.16 in 0.109 seconds.