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.