The generator matrix

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

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+152x^51+193x^52+480x^53+304x^54+734x^55+432x^56+728x^57+307x^58+430x^59+135x^60+128x^61+26x^62+26x^63+6x^64+8x^65+2x^67+2x^70+1x^72+1x^90

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 93.3 seconds.