The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+484x^48+2074x^49+3542x^50+5636x^51+7236x^52+9362x^53+8818x^54+9780x^55+7416x^56+5460x^57+2964x^58+1772x^59+660x^60+194x^61+82x^62+12x^63+27x^64+14x^65+2x^66

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 29.6 seconds.