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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+18x^52+104x^53+45x^54+688x^55+45x^56+104x^57+18x^58+1x^110

The gray image is a code over GF(2) with n=440, k=10 and d=208.
This code was found by Heurico 1.16 in 0.093 seconds.