The generator matrix

 1  0  0  1  1  1 X^2+X  1  1 X^2+X X^2+X  1  1  0  1  1 X^2  X  1  1  1  1  1  X  0  1  0  0 X^2  1  1 X^2  X  0  1 X^2+X  0  1 X^2  1
 0  1  0  0  1 X+1  1 X^2  0 X^2  1 X^2+1 X^2+1  1  1  0  1  0 X+1 X^2+X X^2+1  X  X  1 X^2 X^2+X  1  1  1 X^2+1 X^2  1 X^2+X  1 X^2+X  1  1 X+1  X  0
 0  0  1  1  1  0 X+1  X X^2+X+1  1  0 X^2 X+1 X+1 X+1 X^2+X X^2+X  1  0 X^2 X^2 X^2+X+1 X+1 X^2+X  1 X^2+1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+1  1  0  X  X X^2+X+1  X  1  0
 0  0  0  X  0 X^2  0 X^2 X^2+X  0 X^2  0  0  0  X  X X^2+X X^2+X  X X^2+X  X X^2 X^2+X  X X^2+X X^2 X^2+X X^2  X X^2 X^2  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 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 34.

Homogenous weight enumerator: w(x)=1x^0+35x^34+224x^35+269x^36+536x^37+312x^38+564x^39+347x^40+540x^41+306x^42+428x^43+165x^44+224x^45+80x^46+28x^47+14x^48+12x^49+3x^50+4x^51+2x^52+2x^56

The gray image is a linear code over GF(2) with n=160, k=12 and d=68.
This code was found by Heurico 1.16 in 0.398 seconds.