The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1  2  1  1  2  1  1 X+2  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0  1  0  1  2  0  1  1  X  1  1  X  2  X  0  0  X
 0  1  1 X+2 X+3  1  1 X+1  X  3  1  X  X X+1  1  2 X+1  1  0  1  1  0  1  1  0 X+2  2  X  0 X+2  0 X+2  0 X+2  2  X X+1  1  3  1 X+2  X X+2  1  1 X+1  1  2 X+2  X X+2  0  1  1  1  1
 0  0  X  0 X+2  X  X  2  X  2  0 X+2  0  2 X+2  X  X  0  0 X+2  0 X+2  2 X+2  0  2  X  X  0  2  X  X  2  0 X+2 X+2  0  2  2  0 X+2 X+2 X+2  X  X  X X+2  2  2  0  2  X  2  X  0  X
 0  0  0  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2  0  0  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  2  0  2  0
 0  0  0  0  2  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  2  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  0  2  2  2  0  0  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 52.

Homogenous weight enumerator: w(x)=1x^0+212x^52+244x^54+200x^56+168x^58+138x^60+32x^62+18x^64+2x^68+4x^70+4x^72+1x^80

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 0.166 seconds.