The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^47+1282x^48+3332x^49+6783x^50+12084x^51+20496x^52+29504x^53+37535x^54+38874x^55+38745x^56+29428x^57+20696x^58+12394x^59+6226x^60+2830x^61+1139x^62+348x^63+188x^64+36x^65+23x^66+10x^67+4x^68+6x^69+2x^72

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 480 seconds.