The generator matrix

 1  0  1  1  1 X^2  1  1  0  0  1  1  1  0  1  1  1 X^2 X^2  1  1  X  1  1  X  1  1  1  0  1  1  1 X^2+X  1  1  1 X^2 X^2+X  1 X^2+X
 0  1  1  0  1  1 X^2 X+1  1  1 X^2 X^2+X+1  0  1  1 X+1 X^2  1  1 X^2 X^2+1  1  X  1  1  X X^2+X+1 X^2  1  X X^2+1 X^2+X+1  1 X+1 X^2+X X+1  1  1 X^2+X+1  1
 0  0  X  0  0  0  0 X^2 X^2+X  X X^2+X X^2+X  0  X X^2+X X^2  X  0 X^2 X^2+X X^2+X X^2+X  X X^2  X  X  0 X^2+X  0  0  X X^2 X^2  X X^2 X^2  0  0  0 X^2+X
 0  0  0  X  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2+X X^2+X X^2+X X^2+X  X  X X^2+X  X X^2+X  X  X  X X^2+X X^2  0  0  0  X  0  X  0 X^2+X  0  X X^2  X  X X^2
 0  0  0  0  X X^2+X X^2+X X^2  X  0  0 X^2+X X^2+X X^2 X^2+X  X X^2+X X^2  X  0  0 X^2+X X^2+X  X X^2+X  X X^2+X X^2+X X^2 X^2 X^2 X^2 X^2  0 X^2  X X^2 X^2  0 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+118x^34+92x^35+420x^36+172x^37+672x^38+248x^39+748x^40+248x^41+618x^42+172x^43+347x^44+92x^45+68x^46+42x^48+28x^50+9x^52+1x^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 0.473 seconds.