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  X  0  X  X  1  0  0  X  0  0  1  1  1  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  0  X X^2+X X^2  X  X X^2+X  0 X^2 X^2+X X^2 X^2+X  X X^2 X^2+X  X  X  X  X  X  0 X^2  X  X  X  X X^2  0 X^2+X
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2+X  0 X^2+X X^2+X X^2  0  X X^2 X^2+X  X  0  X  X  X  X  0  X  0 X^2  X X^2 X^2+X  0  X  0 X^2  X  0 X^2+X
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  X X^2+X X^2 X^2  0 X^2  0  0  X X^2+X  0 X^2  0 X^2+X X^2+X  0  X X^2  X X^2+X  X  0  X X^2  X  0  0 X^2  X
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2  0 X^2+X X^2  X  X X^2+X X^2 X^2 X^2 X^2+X  0  X  0  0  X X^2+X X^2+X  0  0  X  X  X X^2+X X^2  X  X X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2

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+206x^34+8x^35+438x^36+48x^37+733x^38+312x^39+1084x^40+672x^41+1293x^42+632x^43+1084x^44+304x^45+643x^46+72x^47+402x^48+188x^50+62x^52+7x^54+1x^58+1x^62+1x^64

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 41 seconds.