The generator matrix

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

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+360x^52+304x^54+354x^56+2x^60+2x^68+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 1.98 seconds.