The generator matrix

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

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+142x^42+716x^43+1752x^44+2626x^45+4134x^46+4524x^47+5114x^48+4508x^49+4392x^50+2502x^51+1265x^52+626x^53+262x^54+96x^55+73x^56+16x^57+14x^58+2x^59+3x^60

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 7.28 seconds.