The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^53+54x^54+104x^55+30x^56+84x^57+30x^58+48x^59+20x^61+10x^62+8x^63+4x^65+2x^66+2x^69+1x^80

The gray image is a code over GF(2) with n=224, k=9 and d=106.
This code was found by Heurico 1.16 in 0.151 seconds.