The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+447x^52+476x^54+487x^56+252x^58+165x^60+100x^62+103x^64+4x^66+11x^68+1x^72+1x^76

The gray image is a code over GF(2) with n=224, k=11 and d=104.
This code was found by Heurico 1.16 in 90.6 seconds.