The generator matrix

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

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+330x^54+144x^55+114x^56+96x^57+308x^58+16x^59+12x^60+1x^64+2x^78

The gray image is a code over GF(2) with n=448, k=10 and d=216.
This code was found by Heurico 1.16 in 0.171 seconds.