The generator matrix

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

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+20x^82+46x^83+43x^84+42x^85+26x^86+12x^87+16x^88+16x^89+6x^90+6x^92+4x^93+4x^95+2x^98+2x^99+5x^100+2x^101+1x^102+1x^104+1x^118

The gray image is a linear code over GF(2) with n=172, k=8 and d=82.
This code was found by Heurico 1.10 in 0 seconds.