The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+277x^44+1040x^45+1142x^46+1498x^47+895x^48+1228x^49+684x^50+776x^51+361x^52+156x^53+78x^54+30x^55+10x^56+8x^57+8x^58

The gray image is a code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 0.485 seconds.