The generator matrix

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

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+249x^32+330x^34+535x^36+548x^38+773x^40+584x^42+554x^44+284x^46+156x^48+46x^50+31x^52+5x^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 1.16 in 42 seconds.