The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+220x^48+1270x^49+3443x^50+6864x^51+12868x^52+20032x^53+29689x^54+35730x^55+41208x^56+35984x^57+31021x^58+20294x^59+12042x^60+6548x^61+3143x^62+1090x^63+439x^64+154x^65+56x^66+18x^67+6x^68+12x^69+8x^70+4x^71

The gray image is a code over GF(2) with n=448, k=18 and d=192.
This code was found by Heurico 1.16 in 478 seconds.