The generator matrix

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

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+168x^52+104x^53+314x^54+304x^55+383x^56+264x^57+256x^58+72x^59+90x^60+16x^61+50x^62+8x^63+12x^64+4x^66+1x^68+1x^92

The gray image is a code over GF(2) with n=448, k=11 and d=208.
This code was found by Heurico 1.16 in 0.203 seconds.