The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^52+108x^53+184x^54+132x^55+152x^56+60x^57+80x^58+36x^59+68x^60+32x^61+12x^62+8x^63+5x^64+8x^65+12x^66+14x^68+2x^72

The gray image is a code over GF(2) with n=224, k=10 and d=104.
This code was found by Heurico 1.11 in 0.0802 seconds.