The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+162x^61+516x^62+580x^63+1170x^64+1380x^65+1698x^66+3000x^67+2442x^68+2330x^69+2916x^70+1626x^71+950x^72+414x^73+276x^74+24x^75+114x^76+78x^77+4x^78+2x^81

The gray image is a linear code over GF(3) with n=306, k=9 and d=183.
This code was found by Heurico 1.16 in 0.723 seconds.