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

generates a code of length 56 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+34x^53+68x^54+128x^55+90x^56+144x^57+4x^58+4x^60+12x^61+23x^62+1x^64+2x^69+1x^78

The gray image is a code over GF(2) with n=448, k=9 and d=212.
This code was found by Heurico 1.16 in 12.4 seconds.