The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+48x^53+386x^54+996x^55+240x^56+772x^57+1758x^58+480x^59+696x^60+960x^61+30x^62+136x^63+30x^66+12x^67+12x^68+2x^72+2x^75

The gray image is a linear code over GF(3) with n=261, k=8 and d=159.
This code was found by Heurico 1.16 in 0.0522 seconds.