The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+276x^53+395x^54+294x^55+270x^56+210x^57+314x^58+182x^59+40x^60+42x^61+1x^62+12x^63+8x^65+1x^66+1x^72+1x^82

The gray image is a code over GF(2) with n=448, k=11 and d=212.
This code was found by Heurico 1.16 in 0.125 seconds.