The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  0  1  1  1  2  1  X X+2  1  1  1  1  X  X  2  1  0  1  1  1 X+2  1  X  1  1  2  2  2  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  0  1 X+1  3  2  1  0  1  1 X+1  2  1  X  1  1  1 X+3  1  X X+3 X+3  1  3  X  2 X+2  1  1  1  0
 0  0  X  0  0  0  0  0  0  2  2  X  X  X  0 X+2  X X+2 X+2 X+2  2 X+2  0  2 X+2 X+2  2 X+2  0  2  2 X+2 X+2  X  2 X+2 X+2  0 X+2  2  X  0
 0  0  0  X  0  0  X  2  X  2 X+2  0  0  0 X+2 X+2 X+2 X+2  X  2  X  0  2  X  2 X+2  2  0  2 X+2 X+2  X  2  X X+2  X  2 X+2  0  2 X+2  0
 0  0  0  0  X  0  0  X  2  2  0  2 X+2  X X+2  2 X+2  X  0  2 X+2 X+2 X+2  2  0  2  X  0  2 X+2  X  X  X  0  0 X+2  X  2 X+2 X+2 X+2  0
 0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  2  2  0  0  0  2  0  2  0  2  2  2  2  0  0  2  2  0  0  0

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+43x^34+106x^35+216x^36+350x^37+510x^38+654x^39+824x^40+990x^41+964x^42+890x^43+801x^44+686x^45+467x^46+266x^47+180x^48+114x^49+56x^50+36x^51+23x^52+4x^53+7x^54+3x^56+1x^58

The gray image is a code over GF(2) with n=168, k=13 and d=68.
This code was found by Heurico 1.16 in 2.39 seconds.