The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+62x^81+71x^82+46x^83+62x^84+66x^85+35x^86+28x^87+39x^88+18x^89+12x^90+10x^91+13x^92+4x^94+4x^95+8x^96+4x^97+1x^98+2x^99+5x^100+10x^101+3x^102+2x^103+2x^107+2x^110+2x^111

The gray image is a linear code over GF(2) with n=172, k=9 and d=81.
This code was found by Heurico 1.16 in 29.9 seconds.