The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+342x^49+1791x^50+3500x^51+7150x^52+9932x^53+15429x^54+17022x^55+20402x^56+18128x^57+15193x^58+9696x^59+6996x^60+2918x^61+1697x^62+582x^63+185x^64+70x^65+12x^66+16x^67+2x^68+2x^69+6x^70

The gray image is a code over GF(2) with n=448, k=17 and d=196.
This code was found by Heurico 1.16 in 121 seconds.