The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+144x^42+800x^43+1634x^44+2574x^45+4027x^46+4710x^47+5206x^48+4832x^49+3928x^50+2396x^51+1342x^52+680x^53+307x^54+110x^55+39x^56+24x^57+10x^58+2x^60+2x^61

The gray image is a code over GF(2) with n=384, k=15 and d=168.
This code was found by Heurico 1.16 in 6.62 seconds.