The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+59x^36+192x^37+339x^38+454x^39+332x^40+592x^41+389x^42+482x^43+279x^44+328x^45+298x^46+196x^47+57x^48+48x^49+29x^50+2x^51+8x^52+8x^53+1x^54+2x^55

The gray image is a code over GF(2) with n=168, k=12 and d=72.
This code was found by Heurico 1.16 in 0.429 seconds.