The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+550x^43+564x^44+876x^45+611x^46+580x^47+297x^48+312x^49+99x^50+118x^51+25x^52+60x^53+1x^54+1x^58+1x^60

The gray image is a code over GF(2) with n=368, k=12 and d=172.
This code was found by Heurico 1.16 in 1.97 seconds.