The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+360x^42+152x^43+768x^44+368x^45+888x^46+352x^47+681x^48+144x^49+336x^50+8x^51+19x^52+8x^54+1x^56+8x^58+1x^60+1x^64

The gray image is a code over GF(2) with n=368, k=12 and d=168.
This code was found by Heurico 1.16 in 74.8 seconds.