The generator matrix

 1  0  0  0  0  1  1  1 X^2  1 X^2+X X^2  1  1  X  1  X  1  X  X  0  1  X  1  1  0  1  1  1  1 X^2  1  0  1  0 X^2+X X^2  1  1  0  1  1
 0  1  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  X X+1  1 X^2+1  1  1  1 X^2+X+1  X  X  1  1 X^2+X+1  1  X X^2+X X^2+X X^2+X+1  1 X+1 X^2+X  1  1 X^2+X+1  X X^2+X X+1  0
 0  0  1  0  0 X^2  1 X^2+1  1  X  X  1 X^2+1 X+1  1 X^2  X  0 X+1 X^2+1 X^2+X+1 X^2+X  1  X  0  X  X X+1 X^2 X^2  1  0  X X^2+1  0 X+1  X X^2 X^2+1 X^2+X  X  0
 0  0  0  1  0 X^2+1  1  0 X^2+1  X  1  X X^2+X  1 X^2+X+1 X+1  1 X^2 X^2  0 X+1 X^2+1  1  1  X  0 X^2+X+1 X^2  1  0 X^2+X X^2+X X^2+1 X+1  1  X X^2+X  0  X  1 X^2 X^2
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  1  1 X+1  X X^2+X+1  0  0 X^2 X^2+X  0 X+1  1 X^2+1 X^2+X  0 X^2+X+1  1  X  1  1  1  1  1 X+1  X  X  X X^2+X X^2+1 X+1 X+1 X^2+1  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+81x^34+480x^35+910x^36+1450x^37+2015x^38+2582x^39+3134x^40+3634x^41+4082x^42+3680x^43+3278x^44+2790x^45+1966x^46+1296x^47+701x^48+406x^49+167x^50+56x^51+40x^52+8x^53+7x^54+2x^55+2x^58

The gray image is a linear code over GF(2) with n=168, k=15 and d=68.
This code was found by Heurico 1.13 in 7.75 seconds.