The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+9x^82+34x^83+48x^84+36x^85+11x^86+16x^87+23x^88+12x^89+6x^90+12x^91+20x^92+12x^93+5x^94+3x^96+4x^97+2x^99+1x^104+1x^154

The gray image is a linear code over GF(2) with n=174, k=8 and d=82.
This code was found by Heurico 1.16 in 0.125 seconds.