The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 0 0 1 X 1 1 1 1 1 X X 1 X 1 1 0 1 1 0 1 X X X 1 1 0
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 X+1 1 1 X X 1 0 X 1 X+1 X 1 X 1 0 1 0 X+1 X 1 1 X+1 X 1
0 0 1 0 0 0 0 0 X X 1 1 1 X 1 X+1 X+1 X+1 X X+1 1 0 X+1 1 X X 1 1 1 X 1 0 1 X X 1 1 0 X+1 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X 1 1 1 X X 1 X+1 1 0 X+1 0 1 X+1 X+1 0 1 X+1 X+1 0 X 1 X 0 X 1
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 X X+1 X+1 0 X+1 1 X+1 X 0 1 0 X 0 0 X X+1 1 0 X 1 1 1 X+1 X X+1 X
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 0 0 0 0 X+1 X X X+1 1 X+1 1 0 X+1 X 0 1 X 1 1 0 1 X X+1 X+1

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+181x^32+428x^34+534x^36+638x^38+607x^40+606x^42+526x^44+314x^46+186x^48+62x^50+12x^52+1x^56

The gray image is a linear code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.10 in 0.468 seconds.