The generator matrix

 1  0  0  1  1  1  X X^2+X  0 X^2  1  1 X^2+X  1  1  1  1  1 X^2  1  X  X  1  1  X  1  1  1  1 X^2+X  0  1  1  1  1  1  1  1  1  1
 0  1  0  X  1 X^2+X+1  1  1  1  X X^2  X  0 X^2+1  1  1 X^2+X+1 X^2+X  1 X^2+X  1 X^2+X X^2+X X+1  1 X^2+X X+1 X^2 X^2+X+1  1  0  0 X+1 X^2+X X^2 X^2 X^2+1 X^2+X X+1  0
 0  0  1  1 X^2+X+1 X^2+X  1 X+1 X^2+X  1  X X^2+X+1  1 X^2+1  X X^2  1  X  1 X^2+X+1  1  1  0 X^2+X+1 X^2  0  0  1 X+1 X+1  1 X^2+1  0  1  X X^2+X X+1 X^2+X X^2  0
 0  0  0 X^2  0  0  0 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 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 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+50x^34+176x^35+381x^36+336x^37+426x^38+436x^39+677x^40+366x^41+340x^42+292x^43+327x^44+126x^45+70x^46+52x^47+18x^48+2x^49+6x^50+4x^51+4x^52+2x^53+4x^54

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 0.39 seconds.