The generator matrix

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

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+10x^54+52x^55+8x^56+40x^57+4x^58+4x^59+6x^60+1x^64+2x^74

The gray image is a code over GF(2) with n=224, k=7 and d=108.
This code was found by Heurico 1.13 in 0.047 seconds.