The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+108x^52+544x^53+642x^54+670x^55+637x^56+492x^57+363x^58+266x^59+116x^60+104x^61+58x^62+60x^63+25x^64+8x^65+1x^68+1x^78

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 0.172 seconds.