The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+132x^49+114x^50+282x^51+462x^52+384x^53+724x^54+1152x^55+2694x^56+1798x^57+2100x^58+4830x^59+1788x^60+1572x^61+570x^62+374x^63+342x^64+150x^65+88x^66+72x^67+6x^68+36x^69+8x^72+4x^75

The gray image is a linear code over GF(3) with n=261, k=9 and d=147.
This code was found by Heurico 1.16 in 1.77 seconds.