The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  1  0  1  0  1  1  X  1  1  1  0  X  1  1  1  1  1  0  1  0  1  0  1  0
 0  1  1  0  1  1  0  1  1  X X+1  1  0 X+1  1 X+1  0  1  0  1 X+1  0  1  1  0  0  1  1  0 X+1 X+1 X+1  X  1 X+1  1  X  1 X+1  X
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  X  0  0  X  0  X  0  X  X  0  X  X  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0  X  X  0  X  0  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  X  0  0  X  X  0  0  0  X  0  X  X  0  X  0  0  X  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  X  X  X  X  0  X  0  0  X  0  0  0  0  X  0  0  X  0  0  0  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  X  X  0  X  X  X  0  X  0  X  X  X  X  0  0  0  X  X  0  X  0  X  X  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  0  0  X  X  X  X  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  0  X  0  X  0  X  X  X  0  0  0  X  X  X  X  0  X  X  X  0  X  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+136x^32+114x^34+317x^36+264x^38+394x^40+284x^42+306x^44+104x^46+89x^48+2x^50+33x^52+4x^56

The gray image is a linear code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.374 seconds.