The generator matrix

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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+72x^50+500x^51+796x^52+622x^53+646x^54+448x^55+370x^56+194x^57+199x^58+120x^59+49x^60+60x^61+9x^62+8x^63+2x^70

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 0.157 seconds.