The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2 X^2+X  1  1 X^2+X X^2+X  1  1 X^2  1  0  0  1  1  1  1  1  0  1  1  1 X^2+X  X  1  0 X^2 X^2 X^2
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1 X^2 X^2+X  1  1  1  0 X^2+1  1  X  0  X X^2+1  1  X  0 X^2  1 X^2+X X^2 X^2+X+1  1 X^2+X X+1  1  1  X  1
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X^2+X+1 X+1  0  X X^2+X X^2+X X^2+X+1  1  1 X^2+X  0 X^2+X+1  1 X^2 X+1 X^2 X^2+X X+1 X^2+X  1 X^2+X  1  1  1  X
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X^2+1 X^2 X+1  X X^2+1 X^2+X X^2  1 X^2+X  X X+1  0 X^2+X+1 X^2+1 X^2+1  1  X X^2+X+1 X^2  0  1 X^2+X+1 X^2 X^2+X X^2
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0 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+154x^34+416x^35+934x^36+1336x^37+2013x^38+2680x^39+3178x^40+3636x^41+3757x^42+3888x^43+3425x^44+2780x^45+1915x^46+1304x^47+737x^48+300x^49+208x^50+32x^51+40x^52+12x^53+15x^54+4x^56+1x^58+1x^60+1x^62

The gray image is a linear code over GF(2) with n=168, k=15 and d=68.
This code was found by Heurico 1.16 in 22.9 seconds.