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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+184x^45+164x^48+404x^51+1002x^54+1728x^57+13122x^58+1716x^60+930x^63+192x^66+144x^69+68x^72+22x^75+4x^78+2x^81

The gray image is a linear code over GF(3) with n=261, k=9 and d=135.
This code was found by Heurico 1.16 in 70.1 seconds.