The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  1  1  1  1  1  1  1  X  1  1  1  1 2X+2  1  X  X  1 2X  0  1 2X+2  1  0  1 2X+2  X  1  1
 0  X  0  X 2X  0 3X+2 X+2  0 2X 3X 3X  0 X+2  2  X  2 3X+2 X+2 2X 2X 3X+2 3X X+2  X 3X 3X  2 3X+2  2 3X 3X+2 2X+2 3X X+2 2X+2  0  2  2  X 3X 3X 2X+2 2X 2X 2X 2X+2  0 3X+2  X  2  X 2X X+2 2X+2
 0  0  X  X  0 X+2 3X+2 2X 2X+2 X+2 X+2 2X+2  2 2X+2  X  X X+2 3X  X 3X  2  0 2X  2  2 3X+2  2 X+2  2 3X+2 2X+2 2X+2  X 3X+2 2X 2X 2X  2  2  2 3X 2X X+2  X  X  X 2X  X  X X+2  X 3X  X 3X 2X+2
 0  0  0 2X+2  2 2X+2 2X 2X+2 2X+2  0 2X+2  2  0  0  2 2X 2X+2  2 2X 2X+2 2X 2X 2X+2  0  2  0 2X+2 2X 2X  2 2X  2 2X 2X 2X+2 2X+2 2X 2X+2 2X 2X  0 2X  0 2X  2 2X+2  2 2X 2X+2 2X 2X+2 2X+2 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+104x^50+276x^51+391x^52+412x^53+714x^54+488x^55+678x^56+374x^57+262x^58+164x^59+85x^60+56x^61+47x^62+16x^63+11x^64+6x^65+8x^66+2x^68+1x^86

The gray image is a code over GF(2) with n=440, k=12 and d=200.
This code was found by Heurico 1.16 in 0.36 seconds.