The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+86x^51+193x^52+306x^53+221x^54+300x^55+165x^56+176x^57+125x^58+114x^59+108x^60+96x^61+56x^62+36x^63+12x^64+24x^65+13x^66+4x^67+1x^68+6x^69+1x^70+4x^71

The gray image is a code over GF(2) with n=224, k=11 and d=102.
This code was found by Heurico 1.16 in 0.204 seconds.