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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+140x^54+214x^57+396x^60+762x^63+1426x^66+13122x^68+1564x^69+1228x^72+466x^75+184x^78+106x^81+54x^84+16x^87+4x^90

The gray image is a linear code over GF(3) with n=306, k=9 and d=162.
This code was found by Heurico 1.16 in 1.72 seconds.