The generator matrix

 1  0  1  1  1  2  1  1  X  X  1  1  2  1  1 X+2  1  1  0  1  1  X  1  1 X+2 X+2  X  X  X  2  2  2  X  2  X X+2  2  0  2  0 X+2  0  X  1  1  1  1  X  1  1  1  1  X  1  0  1
 0  1  1  0 X+1  1 X+3  0  1  1  2  1  1  X X+1  1 X+2 X+1  1  X  1  1  X  3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X X+1  3  1  3 X+3 X+2  3  2  3  X X+2
 0  0  X  0  0  0  0  X X+2 X+2  X  X  2 X+2 X+2 X+2 X+2 X+2  2  2  2 X+2  2  2  X  0  2  0  0  X X+2 X+2  2  X  2 X+2 X+2  X  2  0  2  X  0  2  0  X X+2  X  0  X  2  2 X+2  X  X  0
 0  0  0  X  2 X+2 X+2  X  2 X+2  2 X+2 X+2  0  X  X X+2  2  2 X+2  X  0  2  0  X  0  0  X X+2  0  2  X  2 X+2 X+2  2 X+2  2  2 X+2  X  X  2 X+2 X+2 X+2 X+2  0  0  0  0 X+2  0  X  2  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+232x^52+178x^54+229x^56+220x^58+95x^60+50x^62+9x^64+8x^68+1x^80+1x^84

The gray image is a code over GF(2) with n=224, k=10 and d=104.
This code was found by Heurico 1.16 in 71.7 seconds.