The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+214x^37+443x^38+404x^39+406x^40+436x^41+438x^42+484x^43+381x^44+260x^45+241x^46+164x^47+107x^48+76x^49+28x^50+4x^51+1x^52+6x^53+2x^54

The gray image is a code over GF(2) with n=168, k=12 and d=74.
This code was found by Heurico 1.16 in 18.7 seconds.