The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+366x^44+846x^45+1281x^46+1172x^47+1438x^48+984x^49+796x^50+592x^51+410x^52+162x^53+89x^54+20x^55+25x^56+8x^58+2x^62

The gray image is a code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 0.516 seconds.