The generator matrix

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

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+104x^34+456x^35+936x^36+1300x^37+2196x^38+2356x^39+3429x^40+3644x^41+4043x^42+3416x^43+3589x^44+2510x^45+2109x^46+1230x^47+802x^48+376x^49+149x^50+60x^51+43x^52+10x^53+7x^54+2x^55

The gray image is a code over GF(2) with n=168, k=15 and d=68.
This code was found by Heurico 1.13 in 9.1 seconds.