The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+602x^53+642x^54+960x^55+413x^56+522x^57+220x^58+308x^59+152x^60+162x^61+40x^62+60x^63+1x^64+10x^65+1x^66+1x^72+1x^74

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 144 seconds.