The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+174x^44+438x^45+691x^46+468x^47+773x^48+462x^49+482x^50+274x^51+185x^52+56x^53+43x^54+26x^55+17x^56+4x^57+1x^60+1x^64

The gray image is a code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 0.218 seconds.