The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+508x^50+838x^51+1144x^52+1298x^53+1318x^54+992x^55+819x^56+404x^57+373x^58+278x^59+142x^60+26x^61+40x^62+4x^63+6x^64+1x^66

The gray image is a code over GF(2) with n=432, k=13 and d=200.
This code was found by Heurico 1.16 in 0.609 seconds.