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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+30x^81+12x^82+12x^84+2x^86+2x^88+2x^94+1x^96+2x^97

The gray image is a linear code over GF(2) with n=164, k=6 and d=81.
This code was found by Heurico 1.16 in 53.7 seconds.