The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+26x^81+57x^82+58x^83+51x^84+64x^85+51x^86+40x^87+19x^88+16x^89+28x^90+16x^91+10x^92+4x^93+10x^94+10x^95+8x^96+4x^97+9x^98+2x^99+6x^100+8x^101+3x^102+2x^103+6x^105+2x^106+1x^108

The gray image is a linear code over GF(2) with n=174, k=9 and d=81.
This code was found by Heurico 1.16 in 0.156 seconds.