The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 0 1 1 X^2 X^2 1 1 1 X 1 1 0 X X^2 1 X^2 1 X
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^2 X X 0 X^2+X X X X X^2+X X 0 X X^2+X 0 X^2 X X X X 0
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^2 X X^2 X^2+X X 0 0 X 0 0 0 X^2+X X X^2 X^2 X^2+X 0 X^2+X X X
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 X X^2 X 0 0 X^2 X^2+X 0 X^2+X 0 X^2 X^2 X 0 X^2+X X^2+X X X X^2+X X^2
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 X^2 X^2+X X^2 0 X^2+X 0 X X^2 X^2+X X^2+X 0 X^2+X X X^2 X^2+X X^2+X X^2+X X^2 X^2+X
generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 33.
Homogenous weight enumerator: w(x)=1x^0+80x^33+100x^34+156x^35+91x^36+396x^37+92x^38+324x^39+76x^40+348x^41+56x^42+132x^43+39x^44+68x^45+36x^46+28x^47+14x^48+4x^49+4x^50+2x^52+1x^56
The gray image is a linear code over GF(2) with n=156, k=11 and d=66.
This code was found by Heurico 1.16 in 15.8 seconds.