The generator matrix

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

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+224x^34+68x^35+597x^36+420x^37+1208x^38+1008x^39+1961x^40+1492x^41+2307x^42+1720x^43+1988x^44+972x^45+1128x^46+400x^47+578x^48+60x^49+170x^50+4x^51+55x^52+16x^54+3x^56+3x^58+1x^64

The gray image is a code over GF(2) with n=168, k=14 and d=68.
This code was found by Heurico 1.16 in 74.5 seconds.