The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+170x^41+1092x^42+3074x^43+5934x^44+9826x^45+15640x^46+18776x^47+21886x^48+18882x^49+16018x^50+10050x^51+5665x^52+2542x^53+940x^54+382x^55+125x^56+36x^57+22x^58+4x^59+5x^60+2x^63

The gray image is a code over GF(2) with n=384, k=17 and d=164.
This code was found by Heurico 1.16 in 92.3 seconds.