The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  X X^2  X  0  0 X^2  X X^2  1  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  0  X X^2+X X^2  X  X X^2+X  0 X^2 X^2 X^2+X  X  0 X^2+X  X X^2 X^2  X X^2+X X^2  0  X X^2  X  X X^2+X  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2+X  0 X^2+X X^2+X X^2  0  X X^2 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  X X^2  X X^2 X^2+X X^2 X^2+X  0  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  X X^2+X X^2 X^2  0 X^2  0  0  X  X  X  0 X^2  0  X  0  0  X X^2  0 X^2+X X^2 X^2+X X^2+X  X X^2  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2  0 X^2+X X^2  X  X X^2+X X^2  0 X^2+X  X  0 X^2 X^2+X X^2 X^2+X X^2+X  X  X  X X^2+X  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  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 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  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+212x^32+8x^33+424x^34+48x^35+679x^36+256x^37+1116x^38+712x^39+1331x^40+712x^41+1062x^42+256x^43+735x^44+48x^45+354x^46+8x^47+159x^48+50x^50+17x^52+2x^54+1x^56+1x^60

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 2.84 seconds.