The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  1  X  1  0  1  0  X  X  0  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X X^2  X  0  0  0 X^2  0 X^2+X  X X^2+X  X X^2+X  X  X X^2+X X^2 X^2+X X^2+X  X X^2+X  X X^2+X X^2+X  X  0  0
 0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 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+54x^32+72x^34+32x^35+160x^36+160x^37+120x^38+320x^39+224x^40+320x^41+120x^42+160x^43+145x^44+32x^45+72x^46+39x^48+14x^52+2x^56+1x^60

The gray image is a linear code over GF(2) with n=160, k=11 and d=64.
This code was found by Heurico 1.16 in 0.202 seconds.