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

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+598x^45+632x^46+778x^47+609x^48+470x^49+302x^50+366x^51+128x^52+140x^53+34x^54+16x^55+20x^56+2x^60

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 612 seconds.