The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+620x^50+2070x^51+3745x^52+5442x^53+7339x^54+8916x^55+9453x^56+9274x^57+7334x^58+5188x^59+3227x^60+1708x^61+783x^62+240x^63+110x^64+54x^65+28x^66+2x^67+2x^69

The gray image is a code over GF(2) with n=448, k=16 and d=200.
This code was found by Heurico 1.16 in 29.5 seconds.