The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  1  X  X  1  1  X  X X^2  X  1  X  X X^2  1  X  X  2 X^2  0 X^2  X X^2  X  2 X^2 X^2  2  0  1
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  2  2  0  2  2  0  2  0  2  0  2  0  2  2  0  0  0  2  2  2  0  2  2  0  2  2  0  0  0  0  0  2  2  2  0

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+16x^56+10x^57+2x^58+2x^59+1x^60

The gray image is a code over GF(2) with n=440, k=5 and d=224.
This code was found by Heurico 1.16 in 0.078 seconds.