The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2) 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 0.172 seconds.