The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+28x^53+136x^54+184x^55+125x^56+28x^57+6x^58+1x^60+1x^66+1x^70+1x^72

The gray image is a code over GF(2) with n=440, k=9 and d=212.
This code was found by Heurico 1.16 in 0.079 seconds.