The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1  1  1  1  1 2X^2+X  1  1  1  1 2X  1  1  0  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X+2 2X  1 2X^2+1 2X^2+2X+1  2  1  0 2X 2X^2+X+2 2X^2+X 2X+2  1 2X^2+2X+1 X+1 2X^2+1  0  1 2X^2+1 2X^2+X+2  1 2X 2X^2+X+2 2X+2 X^2+X+2 X+2
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 2X^2 X^2 2X^2  0  0  0  0 X^2  0 2X^2 X^2  0  0
 0  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2  0  0  0 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0  0 X^2 X^2 2X^2 2X^2  0
 0  0  0  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2  0 X^2  0 X^2 X^2  0  0  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+54x^60+168x^61+540x^62+128x^63+1080x^64+2160x^65+172x^66+3594x^67+4374x^68+176x^69+3576x^70+3024x^71+106x^72+234x^73+108x^74+48x^75+96x^76+22x^78+8x^81+14x^84

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 0.625 seconds.