The generator matrix

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

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+368x^51+1042x^52+1600x^53+1982x^54+2228x^55+2479x^56+2054x^57+1875x^58+1300x^59+677x^60+376x^61+204x^62+114x^63+48x^64+18x^65+11x^66+4x^67+1x^68+2x^71

The gray image is a code over GF(2) with n=448, k=14 and d=204.
This code was found by Heurico 1.16 in 2.62 seconds.