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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+8x^85+3x^86+3x^88+1x^94

The gray image is a linear code over GF(2) with n=162, k=4 and d=85.
This code was found by Heurico 1.16 in 0.109 seconds.