The generator matrix

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

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+135x^42+676x^43+1717x^44+2506x^45+4247x^46+4468x^47+5426x^48+4758x^49+4061x^50+2216x^51+1484x^52+622x^53+285x^54+92x^55+41x^56+18x^57+8x^58+4x^59+2x^60+1x^68

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 6.95 seconds.