The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+186x^96+36x^97+36x^98+692x^99+378x^100+522x^101+1880x^102+2268x^103+2250x^104+4884x^105+6354x^106+4338x^107+8182x^108+8208x^109+4176x^110+5946x^111+4374x^112+1800x^113+1700x^114+252x^115+410x^117+96x^120+14x^123+30x^126+12x^129+20x^132+2x^138+2x^147

The gray image is a linear code over GF(3) with n=486, k=10 and d=288.
This code was found by Heurico 1.16 in 8.72 seconds.