The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+772x^63+1500x^64+1380x^65+2648x^66+2532x^67+2400x^68+2450x^69+2346x^70+1116x^71+1630x^72+732x^73+114x^74+22x^75+6x^76+12x^77+10x^78+12x^79

The gray image is a linear code over GF(3) with n=306, k=9 and d=189.
This code was found by Heurico 1.16 in 0.417 seconds.