The generator matrix

1 0 0 0 0 1 1 1 X 1 1 0 1 0 1 1 1 1 X 0 1 1 0 0 X X 1 1 0 X 1 1 0 X X 1 1 1 0 1
0 1 0 0 0 0 0 0 0 1 1 1 X 1 X 1 1 X+1 1 1 X+1 X 1 1 0 X X+1 X X 0 1 X+1 X 1 1 0 0 1 1 0
0 0 1 0 0 0 1 1 1 0 X X 0 X+1 X+1 1 0 X+1 X+1 X+1 X 0 X+1 1 X 1 1 1 1 1 1 0 1 0 X X+1 X+1 X X+1 0
0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 X+1 X X X X 0 1 1 0 X+1 0 1 X 0 X 1 X X+1 X+1 X+1 X+1 X 1 X+1 1 X+1 0
0 0 0 0 1 1 X+1 X 1 X 1 1 0 0 X+1 X X+1 0 X+1 X+1 1 X+1 1 X 0 X X+1 0 0 X+1 X+1 X 0 0 0 X 1 X+1 X 0
0 0 0 0 0 X X 0 0 0 0 X X X 0 0 X X 0 X X 0 0 X X X 0 0 0 0 0 X X 0 X 0 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+47x^32+66x^33+123x^34+142x^35+162x^36+152x^37+142x^38+168x^39+117x^40+164x^41+123x^42+140x^43+129x^44+104x^45+101x^46+56x^47+47x^48+26x^49+22x^50+6x^51+9x^52+1x^54

The gray image is a linear code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.10 in 0.109 seconds.