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  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
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X  2 X^2+X+2  2 X^2+X+2  0 X^2+X X^2+2 X^2 X+2  X X^2+X  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  0  2  2  0  2  2  2  2  0  0  2  0  0  2  0  0  2  2  0  0  0  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  2  2  2  0  0  2  0  0  2  0  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  0  0  2  0  2  2  2  0  0  2  0  0  0  2  0  2  2  0

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+7x^52+32x^53+34x^54+192x^55+495x^56+192x^57+28x^58+32x^59+9x^60+1x^62+1x^110

The gray image is a code over GF(2) with n=448, k=10 and d=208.
This code was found by Heurico 1.16 in 0.156 seconds.