The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+534x^43+770x^44+648x^45+580x^46+576x^47+367x^48+280x^49+152x^50+106x^51+46x^52+28x^53+4x^54+4x^57

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 0.141 seconds.