The generator matrix

 1  0  1  1  1 X+2  1  X  1  2  1  1  1  1 2X  1 X+2  1  1  1 2X+2  1  1  0  1  1  2 3X+2 X+2  1  1  X 3X+2 3X+2 2X  0 X+2 2X+2  1  1  1  1 X+2 3X X+2  X 2X+2 2X+2  1  1  2  X  1  1
 0  1 X+1 3X+2  3  1  2  1 3X+3  1 X+2 2X+3  X 2X+1  1  0  1 3X+1 2X X+1  1 3X  1  1 2X+2 X+3  1  1  1 3X  1  1  1  1  1  1  1  1 2X X+1  0 X+1  1  1  1  1  1  1 3X+2  3  1  1 2X  0
 0  0 2X+2  0  2 2X+2  0 2X+2  2 2X 2X+2  0  2 2X  2 2X  2  2 2X+2  0 2X+2 2X 2X+2  0  2 2X 2X  0 2X  0  2  2  0 2X 2X+2 2X+2  2  2 2X+2  0 2X+2  0 2X  0 2X  0 2X+2  0 2X 2X+2  0  2 2X+2 2X
 0  0  0 2X  0  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X 2X 2X 2X
 0  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0  0  0 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 49.

Homogenous weight enumerator: w(x)=1x^0+92x^49+178x^50+542x^51+197x^52+846x^53+413x^54+846x^55+193x^56+526x^57+155x^58+82x^59+7x^60+2x^61+2x^62+2x^63+2x^64+6x^65+2x^66+1x^78+1x^82

The gray image is a code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.281 seconds.