The generator matrix

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

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+220x^32+368x^34+565x^36+572x^38+667x^40+604x^42+522x^44+340x^46+175x^48+36x^50+25x^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 1.16 in 1.55 seconds.