The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 3X+2  2 2X+2 X+2 2X 3X  X  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 X+1 2X+1  2 X+2 X+3 2X+3 3X 2X 2X+2  X 3X+1  3 3X+3  1  1  1  1  1  1  1  1  1  0 2X X+2 3X+2 2X 2X+2  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0  0  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+24x^52+328x^53+38x^54+240x^55+38x^56+328x^57+24x^58+1x^64+2x^78

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 0.094 seconds.