The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+74x^43+173x^44+400x^45+461x^46+580x^47+686x^48+730x^49+417x^50+290x^51+159x^52+84x^53+14x^54+16x^55+5x^56+2x^57+1x^58+2x^66+1x^70

The gray image is a code over GF(2) with n=384, k=12 and d=172.
This code was found by Heurico 1.16 in 0.25 seconds.