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^2 1 0 0 1 X 1 1 1 1 X^2 1 1 X X 1 1 1 1 X 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 X X X^2+X X X X X^2 X 0 X^2+X X^2 X^2 0 X^2+X 0 X^2+X 0 X^2 0 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 0 X X^2 X^2 X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X X X X^2+X X 0 X^2 X^2 X^2 0 X^2 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 0 X^2 X X^2 X^2+X X X^2 X X^2+X 0 X 0 0 X^2+X 0 X 0 0 X X^2 X^2+X X^2+X X
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 X X^2+X 0 0 X X X 0 0 X X 0 0 X 0 0 X^2+X X 0 X^2
generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+122x^36+236x^38+80x^39+324x^40+192x^41+266x^42+160x^43+286x^44+64x^45+120x^46+16x^47+110x^48+42x^50+20x^52+8x^54+1x^64
The gray image is a linear code over GF(2) with n=168, k=11 and d=72.
This code was found by Heurico 1.16 in 0.192 seconds.