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  X  1  1  X  1  1  X  1  1  1  1  X  1  1  X  X  1  X  1  X  X X^2  0  1  X  X  1 X^2  0  X  X  X  1  1 X^2  0 X^2  X  X X^2  X X^2  0 X^2  X  X  1 X^2 X^2  0  X  X X^2  1  X
 0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+12x^86+3x^88

The gray image is a linear code over GF(2) with n=324, k=4 and d=172.
This code was found by Heurico 1.16 in 0.264 seconds.