The generator matrix

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

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+16x^82+40x^83+12x^84+56x^85+72x^86+14x^88+4x^90+24x^91+2x^92+8x^93+1x^96+4x^98+2x^116

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 0.131 seconds.