The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  1  0  1  1  1  X  1  0  X  0  1  1  1  1  1  1  X  X  X  1  1  1  X  1  X  1  0
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  0  X  1  1  0 X+1  1  1  X  0  X  X  1  0 X+1  1  X  1  1 X+1  X  1  X  X  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  X  1 X+1  1  1  1  0  0  0  1  X X+1 X+1  X  1  0  1  1  1 X+1  X X+1  0  X  1  X  1
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  0  X  X  0  0  0  X  X  X  X  0  X  0  X  X  X  0  X  0  X  0
 0  0  0  0  X  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  X  X  0  0  X  0  0  X  X  X  0  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  X  0  0  0  X  X  X  X  0  0  X  0  X  0  X  X  0  X  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  0  X  0  X  X  X  X  X  0  0  X  X  0  X  0  X  0  0  0  X  0  0  0  0
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X  X  X  0  X  X  0  X  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+49x^32+54x^33+103x^34+152x^35+148x^36+150x^37+163x^38+166x^39+147x^40+170x^41+130x^42+142x^43+124x^44+114x^45+90x^46+50x^47+32x^48+24x^49+23x^50+2x^51+8x^52+3x^54+3x^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 0.309 seconds.