The generator matrix

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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+558x^67+2286x^68+1330x^69+1962x^70+2964x^71+1718x^72+2442x^73+2910x^74+1140x^75+990x^76+1206x^77+98x^78+36x^79+24x^80+6x^81+6x^82+6x^83

The gray image is a linear code over GF(3) with n=324, k=9 and d=201.
This code was found by Heurico 1.16 in 28.7 seconds.