The generator matrix

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

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+194x^48+962x^49+1553x^50+3184x^51+3496x^52+5134x^53+4030x^54+5268x^55+3381x^56+2872x^57+1332x^58+778x^59+258x^60+206x^61+73x^62+16x^63+14x^64+10x^65+1x^66+2x^67+3x^70

The gray image is a code over GF(2) with n=432, k=15 and d=192.
This code was found by Heurico 1.16 in 8.55 seconds.