The generator matrix

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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+536x^96+1742x^99+2726x^102+3070x^105+3400x^108+3486x^111+2500x^114+1556x^117+588x^120+50x^123+24x^126+4x^129

The gray image is a linear code over GF(3) with n=162, k=9 and d=96.
This code was found by Heurico 1.16 in 5.69 seconds.