The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+684x^53+630x^54+732x^55+540x^56+548x^57+252x^58+276x^59+137x^60+200x^61+36x^62+48x^63+1x^64+8x^65+1x^68+2x^70

The gray image is a code over GF(2) with n=448, k=12 and d=212.
This code was found by Heurico 1.16 in 24.8 seconds.