The generator matrix

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

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+371x^50+942x^51+1697x^52+1806x^53+2541x^54+2308x^55+2263x^56+1592x^57+1447x^58+660x^59+368x^60+210x^61+111x^62+24x^63+26x^64+8x^65+2x^66+2x^67+5x^68

The gray image is a code over GF(2) with n=440, k=14 and d=200.
This code was found by Heurico 1.16 in 2.36 seconds.