The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) 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 1.45 seconds.