The generator matrix

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

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+9x^54+54x^55+141x^56+32x^57+6x^58+8x^59+2x^60+2x^71+1x^78

The gray image is a code over GF(2) with n=448, k=8 and d=216.
This code was found by Heurico 1.16 in 0.125 seconds.