The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+14x^54+224x^55+14x^56+1x^64+2x^78

The gray image is a code over GF(2) with n=440, k=8 and d=216.
This code was found by Heurico 1.16 in 0.047 seconds.