The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+348x^46+72x^47+298x^48+48x^49+160x^50+8x^51+66x^52+20x^54+1x^56+1x^60+1x^68

The gray image is a code over GF(2) with n=384, k=10 and d=184.
This code was found by Heurico 1.16 in 1.44 seconds.