The generator matrix

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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+418x^63+486x^64+1692x^65+4806x^66+4770x^67+7704x^68+13824x^69+15282x^70+19602x^71+28966x^72+25380x^73+20826x^74+18222x^75+7758x^76+4122x^77+2628x^78+270x^79+324x^81+66x^84

The gray image is a linear code over GF(3) with n=324, k=11 and d=189.
This code was found by Heurico 1.16 in 32.2 seconds.