The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+174x^51+191x^52+398x^53+503x^54+544x^55+727x^56+436x^57+444x^58+256x^59+122x^60+170x^61+35x^62+44x^63+14x^64+20x^65+10x^66+6x^67+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 0.453 seconds.