The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  0  1  0  1  1  X  X  X  X  1  1  1  1  X  0  1  1  0  0  X  0  1  1  1  X  1
 0  1  0  0  0  0  0  0  0  0  0  0  X  1  1  1  1 X+1 X+1  1  X  1  1  1 X+1  X  1  X  1 X+1 X+1  1  X  X  1  1  1 X+1  0  1
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  0  1 X+1 X+1 X+1  X  1  1  1  0  0  1  0  0  1  X X+1  X  0  1  X  X  1  0  0  1  1
 0  0  0  1  0  0  X  1 X+1  1  0  1  1  0  1  0  X  X  1  0 X+1 X+1  1  0 X+1  X X+1  X  0  1  0  X  1  1  0  X  1  X  X X+1
 0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  X  X  0  0  1  0 X+1  0  1 X+1  1  1  0  1 X+1 X+1  X  0 X+1  1  X  1  1 X+1  0  X  0
 0  0  0  0  0  1  1  X  1  1 X+1  X  1  1  0  X  1 X+1  0  0 X+1  1  X  0  X  0 X+1  1  1 X+1  X  X X+1 X+1  0  0  0  X  0 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+185x^32+432x^34+534x^36+606x^38+614x^40+628x^42+524x^44+320x^46+183x^48+60x^50+6x^52+2x^54+1x^64

The gray image is a linear code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 1.18 seconds.