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.