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  1  1  1  1  1  1  1  1  1  0  X  0  1  0  X  X  1  1  X  X
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  X X^2+X  X X^2+X X^2 X^2  0  X X^2+X  X  X  X X^2+X  0  X X^2+X  0  X  X X^2  X X^2  X X^2  0 X^2+X X^2+X X^2
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2+X X^2+X  0 X^2  X X^2  0 X^2+X X^2+X  X  X  X X^2 X^2 X^2  X  X X^2 X^2  X X^2  X
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X X^2  X  0 X^2 X^2+X X^2 X^2+X  X X^2+X X^2+X X^2+X  X X^2+X X^2 X^2+X X^2 X^2+X  X  X  X X^2+X  X X^2  0  X X^2 X^2  0
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X X^2+X X^2+X X^2 X^2  X  X  0 X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2  X X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2 X^2+X  0 X^2+X X^2
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X X^2 X^2+X X^2  X  0  0 X^2 X^2  0  0  0  0 X^2+X X^2+X  X X^2+X  0  X X^2 X^2+X  X X^2+X  0  X X^2  X X^2+X  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+210x^34+456x^36+40x^37+636x^38+264x^39+1112x^40+720x^41+1322x^42+720x^43+1176x^44+264x^45+606x^46+40x^47+383x^48+156x^50+71x^52+14x^54+1x^68

The gray image is a linear code over GF(2) with n=168, k=13 and d=68.
This code was found by Heurico 1.16 in 4.1 seconds.