The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+248x^56+7x^64

The gray image is a code over GF(2) with n=448, k=8 and d=224.
This code was found by Heurico 1.16 in 0.141 seconds.