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  X  X  1  X  1  X  1  1  1  1  1  1  0 X^2  X  1  1  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X  X  X X^2+X  X  0 X^2+X X^2  X  X  X  0  X X^2+X  X  X X^2 X^2+X X^2 X^2+X X^2+X  0  X  X X^2 X^2  0  0  X
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X  0  0  0 X^2 X^2 X^2+X  X  0  0 X^2+X X^2  0 X^2+X  X X^2  X X^2  X  X X^2  X  X  0 X^2 X^2+X X^2+X X^2
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  0  X  X X^2  X X^2 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X  X  0 X^2+X X^2 X^2+X X^2+X  X X^2+X  X  0  0  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  X X^2 X^2+X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2 X^2  0 X^2+X X^2 X^2  X X^2+X  0  0  X  0  X  0 X^2 X^2+X

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+110x^34+16x^35+182x^36+144x^37+188x^38+352x^39+176x^40+352x^41+102x^42+144x^43+94x^44+16x^45+96x^46+58x^48+16x^50+1x^64

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 0.178 seconds.