The generator matrix

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

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+508x^54+882x^55+396x^56+936x^57+1152x^58+504x^59+1116x^60+882x^61+72x^62+56x^63+36x^66+18x^69+2x^72

The gray image is a linear code over GF(3) with n=261, k=8 and d=162.
This code was found by Heurico 1.16 in 92.1 seconds.