The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2  X  1  1  X  1  1 X^2+X X^2+X X^2  1  X  1 X^2  1  1  1  1  1 X^2+X X^2 X^2  0  1  X  1
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1  X X^2+X  1  1 X^2+X  0  0 X^2  1 X^2+1  1 X+1  1 X^2+X  1 X^2+X X^2+X+1 X^2+1  1 X^2  X X^2 X^2  1  0
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X^2+X+1  X X^2+X+1  X  1  1  1 X^2+X X+1 X^2 X^2 X+1 X+1  0 X^2+X+1 X^2 X^2  1  1  1 X+1 X^2  X
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X^2+1 X^2+X  0 X^2+X X^2+X+1  0  X X^2+X  1 X^2+1 X+1 X^2+1 X^2  X X^2 X+1  0 X^2+X+1 X^2+1 X^2+1  1 X^2+1  0
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 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+142x^32+402x^33+792x^34+1350x^35+1940x^36+2552x^37+3235x^38+3890x^39+3908x^40+3966x^41+3674x^42+2570x^43+1910x^44+1190x^45+596x^46+366x^47+149x^48+80x^49+22x^50+16x^51+14x^52+2x^53+1x^54

The gray image is a linear code over GF(2) with n=160, k=15 and d=64.
This code was found by Heurico 1.16 in 20.8 seconds.