The generator matrix

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

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+170x^34+416x^35+647x^36+724x^37+868x^38+920x^39+859x^40+904x^41+792x^42+752x^43+477x^44+324x^45+206x^46+56x^47+60x^48+10x^50+4x^52+2x^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 1.11 in 0.625 seconds.