The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+180x^64+156x^65+188x^66+300x^67+570x^68+372x^69+264x^70+18x^71+2x^72+18x^73+60x^74+2x^75+42x^76+6x^77+6x^79+2x^93

The gray image is a linear code over GF(3) with n=306, k=7 and d=192.
This code was found by Heurico 1.16 in 0.117 seconds.