The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+20x^54+68x^55+88x^56+56x^57+10x^58+4x^59+6x^60+1x^64+2x^78

The gray image is a code over GF(2) with n=224, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0668 seconds.