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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+120x^54+96x^55+82x^56+96x^57+104x^58+10x^60+1x^64+2x^76

The gray image is a code over GF(2) with n=448, k=9 and d=216.
This code was found by Heurico 1.16 in 0.141 seconds.