The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+216x^50+872x^51+2139x^52+2700x^53+3736x^54+4396x^55+4948x^56+4416x^57+3846x^58+2416x^59+1753x^60+772x^61+240x^62+116x^63+117x^64+48x^65+18x^66+8x^67+10x^68

The gray image is a code over GF(2) with n=448, k=15 and d=200.
This code was found by Heurico 1.16 in 8.01 seconds.