The generator matrix

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

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+344x^49+939x^50+1666x^51+1960x^52+2368x^53+2307x^54+2374x^55+1652x^56+1328x^57+699x^58+404x^59+202x^60+68x^61+37x^62+18x^63+7x^64+4x^65+2x^66+2x^67+2x^68

The gray image is a code over GF(2) with n=432, k=14 and d=196.
This code was found by Heurico 1.16 in 2.3 seconds.