The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+374x^52+296x^54+325x^56+24x^58+2x^60+1x^72+1x^80

The gray image is a code over GF(2) with n=432, k=10 and d=208.
This code was found by Heurico 1.16 in 1.67 seconds.