The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+543x^52+712x^53+1446x^54+1120x^55+1326x^56+856x^57+856x^58+424x^59+442x^60+192x^61+190x^62+24x^63+53x^64+4x^66+3x^68

The gray image is a code over GF(2) with n=448, k=13 and d=208.
This code was found by Heurico 1.16 in 0.593 seconds.