The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+354x^48+1690x^49+3848x^50+6606x^51+9886x^52+14424x^53+18546x^54+20372x^55+18141x^56+15078x^57+10426x^58+6274x^59+3197x^60+1404x^61+550x^62+152x^63+60x^64+40x^65+6x^66+4x^67+9x^68+4x^73

The gray image is a code over GF(2) with n=440, k=17 and d=192.
This code was found by Heurico 1.16 in 120 seconds.