The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+30x^55+144x^56+12x^57+210x^58+288x^59+10x^60+30x^61+2x^63+2x^78

The gray image is a linear code over GF(3) with n=261, k=6 and d=165.
This code was found by Heurico 1.16 in 0.0148 seconds.