The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+686x^51+509x^52+1012x^53+220x^54+712x^55+246x^56+392x^57+56x^58+138x^59+51x^60+60x^61+2x^62+8x^63+1x^64+2x^66

The gray image is a code over GF(2) with n=432, k=12 and d=204.
This code was found by Heurico 1.16 in 57.5 seconds.