The generator matrix

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

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+38x^32+112x^33+224x^34+362x^35+362x^36+674x^37+909x^38+894x^39+1065x^40+938x^41+875x^42+682x^43+406x^44+294x^45+136x^46+106x^47+39x^48+30x^49+28x^50+4x^51+8x^52+3x^54+1x^56+1x^58

The gray image is a linear code over GF(2) with n=160, k=13 and d=64.
This code was found by Heurico 1.16 in 2.04 seconds.