The generator matrix

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

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+20x^50+30x^52+64x^53+288x^54+64x^55+22x^56+10x^58+10x^60+1x^64+2x^74

The gray image is a code over GF(2) with n=432, k=9 and d=200.
This code was found by Heurico 1.16 in 0.078 seconds.