The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1  X  1  1  1  1  1  0  1  2  1  1 X^2+2  1  1  2  1  1 X^2+X+2  1  1  1  1  1  1  1 X^2+X X^2+X+2  1 X^2  1  1  1  1  1 X+2 X^2+X+2  1 X^2  1 X^2+X  1  1  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3 X^2+2  1  X  1  3 X^2+X+1  1 X+1  0  1  2  1 X+1 X^2+2  1 X^2+3  2  1  1 X^2+X+2  1 X^2+3 X^2+X+3  1 X+3 X+3 X^2+X X^2+X+2  1  1 X^2  1 X+2 X^2+X+3 X+1 X+2 X+2  1  1  2  1 X^2+X+2  1  X  0  0 X^2+X+1 X+1 X+1
 0  0 X^2  0  0  0  0  2  2  2  2  2 X^2  2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2 X^2 X^2 X^2  0 X^2+2 X^2+2  0  2 X^2+2  0 X^2+2  2  2 X^2  2  2 X^2+2  0 X^2+2 X^2  0  0  2  2  2 X^2 X^2 X^2+2  2  0
 0  0  0 X^2+2  2 X^2+2 X^2  2  2 X^2 X^2  0  2 X^2+2 X^2 X^2+2 X^2+2  2  2 X^2+2 X^2 X^2  2  0  0  0  0  0 X^2  0 X^2+2  2 X^2  0 X^2  0 X^2+2 X^2+2 X^2+2 X^2+2  2 X^2+2  2  2  2 X^2 X^2 X^2 X^2  2 X^2+2  2  0  2  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+396x^52+224x^53+704x^54+288x^55+900x^56+288x^57+704x^58+224x^59+348x^60+16x^68+2x^72+1x^80

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 32.5 seconds.