The generator matrix

 1  0  1  1 2X+2  1  1  1 3X+2  1  1  2  0  1  1  1  1  1  2  2  1  1  1  0 2X 3X  X X+2  0  X X+2 3X+2 3X  1  1 2X  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1 2X X+2  1
 0  1  1 3X+2  1 3X+3 2X+2 2X+3  1 X+1  X  1  1 2X+2 X+1 2X  X  1  1  1 X+3 X+2  3  1  1  1  1  1  0  1  1  1  1  0 3X+2 2X+2 X+3 2X+3  X 3X+2  2 X+1  1  0 3X+3 X+2 2X X+3 2X+3  1 2X+1  1  1 2X
 0  0  X  0 3X  X 3X 2X  0 2X 3X X+2  2 X+2  2 2X+2 X+2 3X+2 X+2  X 3X+2 2X+2  2  0 2X+2 2X  X  X  X X+2 3X+2  2  2 3X+2 X+2  X 2X 3X+2 2X+2 3X 2X X+2 3X  X  X  0  2 2X+2  2  X 2X+2 3X  0  X
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X  0 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+185x^50+438x^51+734x^52+564x^53+547x^54+548x^55+428x^56+280x^57+178x^58+70x^59+76x^60+20x^61+24x^62+1x^66+1x^70+1x^72

The gray image is a code over GF(2) with n=432, k=12 and d=200.
This code was found by Heurico 1.16 in 0.281 seconds.