The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+56x^52+460x^53+716x^54+792x^55+718x^56+446x^57+333x^58+188x^59+71x^60+114x^61+113x^62+64x^63+16x^65+6x^66+2x^68

The gray image is a code over GF(2) with n=448, k=12 and d=208.
This code was found by Heurico 1.16 in 0.172 seconds.