The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  0  1  1  1 X^2  1  X X^2+X  1  1  1  1  X  X X^2  1 X^2  1  1  1  1  X  1  X  1  X  1
 0  1  1  0  1  1  X X^2+X+1  1 X^2+X  1 X^2+X+1  0  1 X+1 X^2+1 X^2  1  0  1  1 X+1 X^2  1  X  1  1  1  X  1  X X^2+X+1 X^2+X  1 X^2 X^2+X X^2+X X^2+X  X  0
 0  0  X  0  0  0  0  0  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^2 X^2+X X^2+X  X X^2+X X^2 X^2+X  X X^2+X  0  X X^2 X^2+X X^2  0  X  0
 0  0  0  X  0  0  X X^2  X X^2 X^2+X  0  0  0 X^2+X X^2+X X^2+X X^2+X  X X^2  X  0 X^2  X X^2 X^2+X  X  0 X^2+X X^2+X X^2 X^2  X  X  X X^2  X X^2  X  0
 0  0  0  0  X  0  0  X X^2 X^2  0 X^2 X^2+X  X X^2+X X^2 X^2+X  X  0 X^2 X^2+X X^2+X X^2+X X^2  0 X^2  0 X^2  X X^2+X X^2  X  X X^2+X  0  0 X^2 X^2 X^2+X  0
 0  0  0  0  0 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 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 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+56x^32+98x^33+202x^34+338x^35+525x^36+724x^37+779x^38+912x^39+1015x^40+912x^41+774x^42+684x^43+485x^44+284x^45+158x^46+112x^47+56x^48+30x^49+36x^50+2x^51+6x^52+3x^54

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 2.21 seconds.