The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+618x^49+2034x^50+3518x^51+5584x^52+7328x^53+9042x^54+9620x^55+9025x^56+7346x^57+5526x^58+3116x^59+1632x^60+734x^61+266x^62+92x^63+36x^64+4x^65+4x^66+6x^67+2x^68+2x^69

The gray image is a code over GF(2) with n=440, k=16 and d=196.
This code was found by Heurico 1.16 in 30.7 seconds.