The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  1 X^2  1  0  1  1  X X^2+X X^2+X  1 X^2  0  1  1  1  1 X^2 X^2  X  1  1 X^2 X^2+X  1  0  X X^2 X^2+X  1  0
 0  1  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  1  1  1  1  1  1 X+1 X^2+X+1 X^2+1 X^2+X X^2+X  1 X^2+X  X  1  X  1 X^2+X+1  X  1  1  X X^2+1  1
 0  0  1  0  0  0  0 X^2 X^2  1  1  1 X+1  1  1  X X^2+X X^2+1 X+1 X+1  1  X X^2+X X^2+1 X^2+X X+1  1  0  1 X^2 X^2  0 X^2+X+1 X+1 X^2+X  1 X^2  X X^2+X+1  1
 0  0  0  1  0  1  X X+1  1  1 X^2 X^2+1 X^2+X+1 X^2+1 X^2+X X^2+1 X^2+1 X^2+X+1 X^2+1 X^2+X+1  0 X^2 X^2+X  0  0 X^2+X  0 X+1 X^2 X+1  1  1 X^2+X X+1 X^2  0 X^2+X  1  X X^2+X+1
 0  0  0  0  1  1 X+1  X X+1 X^2 X^2+1  1  1  X  X X^2+X  1 X^2+X X^2+X+1 X^2+1  0  1 X^2+1 X^2+X  X X^2+X  1  X X^2+X X+1  X X^2+X X^2 X^2  1 X+1 X^2+X+1  1 X^2 X^2
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  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+360x^32+784x^33+1712x^34+2408x^35+4024x^36+4892x^37+6966x^38+7052x^39+8516x^40+7628x^41+7252x^42+4888x^43+4143x^44+2408x^45+1386x^46+540x^47+386x^48+92x^49+56x^50+24x^51+9x^52+4x^53+4x^54+1x^56

The gray image is a linear code over GF(2) with n=160, k=16 and d=64.
This code was found by Heurico 1.13 in 29.3 seconds.