The generator matrix

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

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+564x^60+108x^61+1026x^62+2510x^63+1476x^64+4194x^65+7080x^66+4806x^67+10584x^68+11142x^69+4968x^70+5886x^71+3350x^72+306x^73+180x^74+660x^75+192x^78+16x^81

The gray image is a linear code over GF(3) with n=306, k=10 and d=180.
This code was found by Heurico 1.16 in 4.56 seconds.