The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+480x^55+300x^56+10x^57+450x^58+414x^59+10x^60+468x^61+36x^62+2x^63+6x^64+6x^65+2x^66+2x^69

The gray image is a linear code over GF(3) with n=261, k=7 and d=165.
This code was found by Heurico 1.16 in 9.22 seconds.