The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+282x^34+288x^35+703x^36+552x^37+998x^38+696x^39+1211x^40+704x^41+1012x^42+576x^43+613x^44+216x^45+210x^46+40x^47+60x^48+22x^50+4x^52+4x^54

The gray image is a linear code over GF(2) with n=160, k=13 and d=68.
This code was found by Heurico 1.16 in 28.1 seconds.