The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+178x^47+1209x^48+3212x^49+7138x^50+11904x^51+20917x^52+29020x^53+36553x^54+41152x^55+37400x^56+29524x^57+20766x^58+12018x^59+6735x^60+2610x^61+1175x^62+386x^63+164x^64+30x^65+30x^66+10x^67+6x^68+2x^69+2x^70+2x^73

The gray image is a code over GF(2) with n=440, k=18 and d=188.
This code was found by Heurico 1.16 in 447 seconds.