The generator matrix

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

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+220x^43+998x^44+1458x^45+1859x^46+2352x^47+2939x^48+2230x^49+1914x^50+1156x^51+667x^52+342x^53+171x^54+36x^55+18x^56+2x^57+8x^58+10x^59+1x^60+2x^67

The gray image is a code over GF(2) with n=384, k=14 and d=172.
This code was found by Heurico 1.16 in 1.94 seconds.