The generator matrix

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

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+272x^54+58x^56+128x^58+48x^62+3x^64+2x^72

The gray image is a code over GF(2) with n=224, k=9 and d=108.
This code was found by Heurico 1.16 in 1.72 seconds.