The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+179x^52+540x^53+525x^54+696x^55+568x^56+588x^57+341x^58+220x^59+191x^60+156x^61+28x^62+36x^63+20x^64+4x^65+1x^70+1x^72+1x^74

The gray image is a code over GF(2) with n=448, k=12 and d=208.
This code was found by Heurico 1.16 in 0.297 seconds.