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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+74x^54+864x^56+112x^57+972x^59+6x^63+108x^65+48x^66+2x^84

The gray image is a linear code over GF(3) with n=261, k=7 and d=162.
This code was found by Heurico 1.16 in 0.0183 seconds.