The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2 X^2  1  1  X  1 X^2  1  X  X  1  X  X  1  X  1  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  0  X  X X^2+X X^2 X^2+X  X  X  0 X^2+X X^2 X^2  0  0  0  X  X X^2 X^2  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2 X^2  0  0  X X^2+X  X  X X^2 X^2  0  X X^2 X^2+X X^2+X  X X^2+X X^2+X  X X^2  0  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X X^2+X X^2+X X^2+X  0  X  0  X X^2 X^2+X  0  X  X X^2+X X^2 X^2+X  X X^2 X^2 X^2+X  X  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+61x^32+66x^33+124x^34+202x^35+121x^36+426x^37+139x^38+846x^39+143x^40+874x^41+135x^42+414x^43+141x^44+150x^45+86x^46+66x^47+39x^48+20x^49+25x^50+8x^51+6x^52+2x^54+1x^62

The gray image is a linear code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.627 seconds.