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

generates a code of length 56 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+132x^51+260x^52+362x^53+608x^54+440x^55+682x^56+442x^57+498x^58+260x^59+163x^60+86x^61+60x^62+48x^63+19x^64+22x^65+10x^66+2x^68+1x^84

The gray image is a code over GF(2) with n=448, k=12 and d=204.
This code was found by Heurico 1.16 in 0.375 seconds.