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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+33x^78+45x^80+96x^81+32x^85+30x^86+18x^88+1x^158

The gray image is a linear code over GF(2) with n=164, k=8 and d=78.
This code was found by Heurico 1.16 in 0.109 seconds.