The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+542x^48+1980x^49+3684x^50+5358x^51+7564x^52+8518x^53+10056x^54+9062x^55+7965x^56+5002x^57+3074x^58+1672x^59+662x^60+238x^61+100x^62+34x^63+10x^64+6x^65+6x^66+2x^67

The gray image is a code over GF(2) with n=432, k=16 and d=192.
This code was found by Heurico 1.16 in 30.8 seconds.