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

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+108x^60+60x^61+18x^62+212x^63+264x^64+108x^65+736x^66+744x^67+1674x^68+1284x^69+762x^70+144x^71+162x^72+78x^73+108x^75+30x^76+42x^78+6x^79+8x^81+6x^87+4x^90+2x^93

The gray image is a linear code over GF(3) with n=306, k=8 and d=180.
This code was found by Heurico 1.16 in 0.13 seconds.