The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  1  0  2  1  1 X+2 X+2  1 X+2  1  1  1 X+2 X+2  1  1  X  1  1  X  1  1  1  1  1  X  1  X  2  0 X+2  1  1  1  0  1  1  1  X  1 X+2  2
 0  1  0  0  3  3  1 X+2  1  1  X X+3  X X+1 X+2 X+2  1  1 X+3  1  1 X+2  X  2  3  2  1  1  X X+1 X+2  3 X+2  2  X X+2 X+1 X+3  3  1  3  1  1  1  1 X+3 X+1  1  1  2  2  0  0  0  1  0
 0  0  1 X+1 X+3  2 X+3  1 X+2  1  X  3  1  2  0  1 X+1 X+2  1  0 X+3 X+1  1  X  0  3  X  3 X+2  2  1 X+3 X+3  1  0  1  X X+1  1 X+2 X+2  1  0 X+2  2 X+2 X+3  1  1  2  X  1  1 X+1 X+3  1
 0  0  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  0  2  0  2  0  2  0  2  2  2  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  2  0  2  0  0  2  2  2  2  0  2  0  0  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+672x^54+120x^56+224x^62+7x^64

The gray image is a code over GF(2) with n=224, k=10 and d=108.
This code was found by Heurico 1.16 in 99.4 seconds.