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  X  X  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  X  X  0  0
 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  X  X  0  0  0
 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  X  X  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  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  0  X  X  X  X
 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  X  0  X  0  0

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+33x^76+141x^80+62x^84+18x^88+1x^156

The gray image is a linear code over GF(2) with n=162, k=8 and d=76.
This code was found by Heurico 1.16 in 0.115 seconds.