The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+120x^84+90x^88+33x^92+4x^96+1x^100+3x^104+2x^108+2x^112

The gray image is a linear code over GF(2) with n=174, k=8 and d=84.
This code was found by Heurico 1.16 in 16.7 seconds.