The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+216x^41+1121x^42+3024x^43+6033x^44+9574x^45+15731x^46+18496x^47+22277x^48+18442x^49+16552x^50+10216x^51+5461x^52+2318x^53+1037x^54+384x^55+112x^56+38x^57+19x^58+8x^59+4x^60+4x^61+2x^62+2x^66

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 95.6 seconds.