The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+47x^50+104x^51+102x^52+224x^53+377x^54+402x^55+363x^56+208x^57+77x^58+52x^59+32x^60+24x^61+19x^62+2x^63+5x^64+8x^65+1x^96

The gray image is a code over GF(2) with n=440, k=11 and d=200.
This code was found by Heurico 1.16 in 0.187 seconds.