The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^50+466x^51+666x^52+870x^53+606x^54+446x^55+380x^56+178x^57+110x^58+124x^59+60x^60+80x^61+12x^62+12x^63+5x^64

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 0.172 seconds.