The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+300x^42+1642x^43+3175x^44+5448x^45+7481x^46+9656x^47+10259x^48+9882x^49+7419x^50+5318x^51+2877x^52+1396x^53+398x^54+180x^55+70x^56+10x^57+15x^58+4x^59+2x^60+3x^62

The gray image is a code over GF(2) with n=384, k=16 and d=168.
This code was found by Heurico 1.16 in 26.2 seconds.