The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+242x^48+1120x^49+3539x^50+7250x^51+12623x^52+19552x^53+30184x^54+35276x^55+41629x^56+36174x^57+30855x^58+19634x^59+12701x^60+6664x^61+2909x^62+1106x^63+404x^64+168x^65+60x^66+28x^67+12x^68+3x^70+2x^71+4x^72+2x^73+2x^74

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 481 seconds.