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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+516x^60+108x^62+1352x^63+270x^64+432x^65+2628x^66+1404x^67+4644x^68+4182x^69+1242x^70+648x^71+1444x^72+648x^75+144x^78+18x^81+2x^90

The gray image is a linear code over GF(3) with n=306, k=9 and d=180.
This code was found by Heurico 1.16 in 0.919 seconds.