The generator matrix

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

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+100x^51+233x^52+250x^53+272x^54+222x^55+179x^56+172x^57+120x^58+154x^59+97x^60+60x^61+58x^62+44x^63+48x^64+12x^65+12x^66+6x^67+2x^68+2x^69+2x^70+2x^71

The gray image is a code over GF(2) with n=224, k=11 and d=102.
This code was found by Heurico 1.11 in 0.127 seconds.