The generator matrix

 1  0  1  1 2X+2  1  1  1 3X+2  1  1  X  1  1 2X+2  1  1 2X  1  1  1  1  X  1  1 X+2  1  1  1  1  1  1  1 X+2  1 X+2  1  1  2 2X+2  1  1  1  1  X  1
 0  1  1 3X+2  1 3X+3 2X+2 2X+3  1 3X X+1  1 2X+2 3X+3  1 3X+2 2X+3  1 X+1  1 3X+1 2X+1  1 2X  X  1 X+1  1 3X+1 X+1 2X+1  1  0  1 2X  1  X 3X  1  1  2  2  0 3X 2X  2
 0  0  X  0 3X  X 3X 2X  0 X+2 2X  X X+2 3X+2 X+2 2X+2  2  2 3X+2 2X+2 3X 2X X+2  2  X 2X+2  0  X 2X+2 2X+2 3X+2 X+2 3X+2 3X 2X+2  2 2X+2 3X 2X 3X 2X 3X 3X 2X+2 3X+2 3X+2
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  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+160x^42+330x^43+858x^44+552x^45+474x^46+476x^47+744x^48+256x^49+152x^50+26x^51+28x^52+24x^53+12x^54+1x^56+1x^58+1x^66

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 0.187 seconds.