The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+62x^49+379x^50+560x^51+695x^52+632x^53+772x^54+704x^55+791x^56+758x^57+684x^58+586x^59+593x^60+316x^61+312x^62+152x^63+108x^64+56x^65+13x^66+10x^67+4x^68+4x^71

The gray image is a code over GF(2) with n=224, k=13 and d=98.
This code was found by Heurico 1.13 in 1 seconds.