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  X  X  1  X  1  1  1  1  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  X  X  0  X  X  X  0  X  X  X  X  X  0  X  0  X  X  X  X  0  X  0  X  0  X  X  X  X  X  X  0  0  0  0  0  0  0  X  X  0  X  X  0  0  X  0  X  X  X  0  0  0  0  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  0  X  0  X  0  X  0  X  X  X  0  X  X  X  0  X  X  X  0  X  X  X  0  X  X  X  0  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  X  0  X  X  X  X  0  0  0  0  X  0  0  X  X  0  0  X  X  X  X  X  X  X  0  X  0  0  0  0  X  0  X  X  0  0  0  X  X  0  0  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  X  0  0  X  0  0  0  X  X  0  0  0
 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  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  X  0  X  X  0  X  X  X  0  X  X  X  X  0  X  0  X  X  X  0  X  X  X  0  0  0  X  X  0  0  0  0  X  X  0  0  X  0  0  X  X  X  X  X  X  0  X  0  0
 0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  X  0  X  X  0  0  0  0  0  0  0  0  X  X  0  0  X  0  X  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  0  0  X  X  0  0  X  X  0  X  X  0  0  X  0  0  0  X  0  0
 0  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  0  0  X  X  X  X  X  0  X  X  X  0  0  0  X  X  X  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  X  X  X  X  0  X  X

generates a code of length 90 over Z2[X]/(X^2) who�s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+26x^84+90x^88+48x^90+47x^92+16x^94+21x^96+6x^100+1x^172

The gray image is a linear code over GF(2) with n=180, k=8 and d=84.
This code was found by Heurico 1.16 in 0.165 seconds.