The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+120x^57+72x^59+310x^60+72x^61+330x^62+494x^63+252x^64+1230x^65+3642x^66+432x^67+2328x^68+6650x^69+522x^70+1668x^71+710x^72+180x^73+174x^74+306x^75+30x^77+86x^78+40x^81+18x^84+10x^87+6x^90

The gray image is a linear code over GF(3) with n=306, k=9 and d=171.
This code was found by Heurico 1.16 in 1.01 seconds.