The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X  X  0  X  0  X  0  X  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  0  0  0  0  X  X  X  0  X  0  X  X  0  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  0  0  X  X  X  X  X  X  X  X  X  X  0  X  0  X  0  X  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  0  0  0  X  X  X  X  X  X  0  X  0  0  0  0  X  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  X  X  0  0  0  X  X  0  0  0  X  X  X  0  0  0  X  X  0  X
 0  0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  0  0  0  0  0  X  X  0  X  0  X  0  0  X  0  X  0  X  X
 0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  0  0  X  0  0  X  X
 0  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  0  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+50x^84+32x^86+104x^88+32x^90+21x^92+15x^96+1x^172

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 43.3 seconds.