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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+6x^86+7x^88+2x^90

The gray image is a linear code over GF(2) with n=164, k=4 and d=86.
This code was found by Heurico 1.16 in 0.123 seconds.