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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+65x^82+65x^84+38x^86+32x^88+19x^90+20x^92+5x^94+7x^96+2x^100+1x^102+1x^148

The gray image is a linear code over GF(2) with n=172, k=8 and d=82.
This code was found by Heurico 1.16 in 0.935 seconds.