The generator matrix

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

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+64x^51+63x^52+184x^53+54x^54+172x^55+50x^56+116x^57+30x^58+136x^59+34x^60+80x^61+10x^62+12x^63+8x^64+4x^65+2x^66+1x^68+1x^72+1x^76+1x^84

The gray image is a code over GF(2) with n=224, k=10 and d=102.
This code was found by Heurico 1.16 in 0.12 seconds.