The generator matrix

 1  0  0  0  1  1  1  0  1  X  1  0  1  X  1  1  1  1  1  1  0  X  1  0  1  0  1  1  0  1  1  X  1  1  0  1  1  0  1  1
 0  1  0  0  0  1  1  1 X+1  X  0  1  X  1  X  X X+1 X+1  X  X  1  X  X  1 X+1  1  X  X  1  1  1  1  X  1  1  1  0  1  1  0
 0  0  1  0  1  1  0  1  1  1  X  0 X+1  1 X+1  X  0  0  X  0  0  1  X X+1  1  1 X+1  X  0 X+1 X+1 X+1  1 X+1  X  0  0  1  0  0
 0  0  0  1  1  0  1 X+1  1 X+1 X+1 X+1  X  0  0  X  X X+1 X+1  0 X+1 X+1  0 X+1  1  0 X+1  X  0  0  X  X X+1  0  1  0  1 X+1 X+1  0
 0  0  0  0  X  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  X  0  X  0  0  0  X  X  X  X  0  X  X  X  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  0  X  X  0  X  X  X  0  0  0  X  X  0  X  X  0  X  0  0  0  X  0
 0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  X  X  X  0  0  X  X  X  0  0  X  X  0  X  X  X  X  X  X  X  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+67x^32+74x^33+113x^34+138x^35+123x^36+142x^37+148x^38+150x^39+142x^40+178x^41+144x^42+154x^43+119x^44+106x^45+85x^46+66x^47+49x^48+12x^49+18x^50+4x^51+10x^52+3x^54+1x^56+1x^58

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 0.291 seconds.