The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  X  1  1 X^2+X  0  X  1  1  X  1 X^2+X  1 X^2+X  1  1 X^2  1  1  1  0  1  1  1 X^2+X X^2+X  1  0 X^2  1
 0  1  0  0  0  1 X^2 X^2+1  1 X+1 X^2+X  1 X^2+1 X^2+X  1  1  X X^2  0  X X+1  1 X^2+1  1  X  1  1 X^2+X X^2 X+1  1  1 X^2+X+1 X^2+X+1  1  1 X^2+X+1  X  1 X^2
 0  0  1  0  0  1 X^2+1  X X^2+X+1 X^2+1  1 X^2 X^2+X X+1 X^2+1 X^2+X+1  1 X^2+X+1 X+1  X X+1  0 X^2+X  0 X^2 X+1  0 X^2+1  X  0 X^2+1 X^2 X^2+X X+1  1  1  X  1  X X^2+X
 0  0  0  1 X+1 X^2 X^2+X+1 X^2+1 X^2+1  1  1 X^2+1  X X^2+X  0  0 X^2+X+1  1 X^2+X  1  X X^2 X^2 X^2+X+1  1 X^2+X+1 X+1  X  0 X+1 X^2+X X^2 X^2+X+1 X^2  X X^2+X+1 X^2+X X^2 X^2 X^2+X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  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+185x^34+396x^35+671x^36+696x^37+834x^38+896x^39+1004x^40+860x^41+848x^42+548x^43+589x^44+328x^45+171x^46+112x^47+37x^48+4x^49+9x^50+2x^52+1x^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 1.43 seconds.