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

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+542x^45+634x^46+912x^47+501x^48+540x^49+299x^50+312x^51+144x^52+134x^53+16x^54+56x^55+2x^56+3x^58

The gray image is a code over GF(2) with n=384, k=12 and d=180.
This code was found by Heurico 1.16 in 7.86 seconds.