The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X X^2 0 X 1 X 1 0 1 1 X 0 1 1 0 X X X
0 X 0 0 0 0 0 0 0 X X^2+X X X^2 X^2 X 0 X^2 X X^2+X X^2 X X^2+X X 0 X 0 X X X^2 X^2 X^2+X X X 0 X^2 X X^2+X X^2+X X X^2 0 0
0 0 X 0 0 0 X X^2+X X X X 0 0 X X^2 X X^2 X X^2+X X^2 X^2+X 0 X^2+X X X^2 X^2 X^2 X^2 X^2+X X^2 X X^2 0 X^2 0 0 X^2 X X^2 X^2 X^2 X
0 0 0 X 0 X X X X^2 0 0 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X X 0 X^2 X X 0 X^2+X X^2 0 X 0 0 X^2+X X^2+X 0 X X^2+X X 0 X^2 X
0 0 0 0 X X X^2 X^2+X X^2+X 0 X X 0 X^2+X X X^2 X X X^2 X^2+X 0 0 X^2 0 X^2 X^2+X X^2 0 X X^2+X 0 X^2+X X^2+X 0 X^2+X X^2 X X X^2+X X^2+X X^2+X 0
0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0
generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+48x^34+88x^35+130x^36+194x^37+221x^38+360x^39+395x^40+420x^41+492x^42+410x^43+366x^44+288x^45+208x^46+166x^47+119x^48+76x^49+48x^50+30x^51+12x^52+14x^53+7x^54+2x^55+1x^56
The gray image is a linear code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 0.679 seconds.