The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1 X^2  X  1  X  1  1  1  1  X  1  0  1  0  1  0  X  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X  X X^2  X X^2+X  X X^2 X^2+X X^2  X  X  0 X^2+X  X X^2  0 X^2  X  X  X  0
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X X^2  0 X^2+X  X  X X^2+X  X  X X^2+X X^2+X X^2+X  0  X X^2+X  X  0 X^2  0 X^2  0
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2+X  0 X^2+X X^2 X^2+X X^2 X^2 X^2+X  X  0 X^2+X X^2+X X^2  0  X X^2 X^2  X  0
 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 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 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+108x^34+16x^35+239x^36+80x^37+307x^38+160x^39+325x^40+160x^41+247x^42+80x^43+150x^44+16x^45+89x^46+46x^48+17x^50+6x^52+1x^60

The gray image is a linear code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.189 seconds.