The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+320x^42+1600x^43+3286x^44+5514x^45+7245x^46+9756x^47+9674x^48+10418x^49+7812x^50+5192x^51+2544x^52+1368x^53+541x^54+172x^55+47x^56+26x^57+18x^58+2x^61

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 24.4 seconds.