The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X+2  X  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  1 X^2+1  3 X+1 X+3 X^2+3  3  1 X+1 X^2+X+3 X^2+X+1 X+1 X^2+1 X+3  0  2 X^2+X+3 X^2+3 X+2  1  1  0
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  0  0  0  2  2  2  0  0  0  2  2  0  2  2  2  0  0  2  0  0  2
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  2
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  0  2  0  2  0  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+118x^52+192x^53+211x^54+384x^55+259x^56+400x^57+169x^58+160x^59+132x^60+16x^61+2x^62+1x^64+1x^70+1x^80+1x^82

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 0.141 seconds.