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  1  1  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X X^2  X X^2+2X 2X^2 2X^2+2X X^2 X^2  0 2X^2+2X X^2+2X X^2+X X^2+2X X^2 2X^2+X 2X^2+X  X X^2+2X 2X^2+X  X X^2+X
 0  0  X 2X X^2 2X^2+2X X^2+X  X 2X^2+2X 2X^2 X^2+X  0 2X^2+X X^2+X 2X 2X^2+2X  X 2X^2+2X X^2+2X 2X  X 2X^2 X^2 2X X^2 X^2 X^2+X X^2+X 2X^2+X
 0  0  0 X^2  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 X^2  0 X^2 2X^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 52.

Homogenous weight enumerator: w(x)=1x^0+228x^52+320x^54+336x^55+138x^57+4728x^58+52x^60+312x^61+138x^63+204x^64+78x^66+24x^67+2x^87

The gray image is a linear code over GF(3) with n=261, k=8 and d=156.
This code was found by Heurico 1.16 in 24.1 seconds.