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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+50x^86+47x^88+28x^90+32x^92+18x^94+10x^96+1x^104+1x^160

The gray image is a linear code over GF(2) with n=176, k=8 and d=84.
This code was found by Heurico 1.16 in 0.125 seconds.