The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+546x^45+604x^46+926x^47+489x^48+598x^49+302x^50+298x^51+102x^52+148x^53+35x^54+32x^55+12x^57+2x^58+1x^62

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 0.156 seconds.