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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+36x^87+24x^88+16x^89+26x^90+8x^91+4x^92+4x^94+2x^95+3x^96+1x^98+2x^111+1x^114

The gray image is a linear code over GF(2) with n=178, k=7 and d=87.
This code was found by Heurico 1.16 in 48 seconds.