The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  X  0  1  X  0  1  1  1  1  X  1  1  1  X  0  X  X  X  X  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  X  0 X^2+X X^2+X  X X^2+X X^2+X  X  0 X^2  X X^2+X X^2+X  0  0  0 X^2+X  X X^2+X X^2 X^2+X  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  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  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 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 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0  0 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 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+132x^28+62x^30+492x^32+576x^34+128x^35+1606x^36+640x^37+1926x^38+1280x^39+2688x^40+1280x^41+1920x^42+640x^43+1652x^44+128x^45+570x^46+478x^48+64x^50+94x^52+2x^54+20x^56+4x^60+1x^64

The gray image is a linear code over GF(2) with n=160, k=14 and d=56.
This code was found by Heurico 1.16 in 9.65 seconds.