The generator matrix

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

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+810x^53+800x^54+1464x^55+3270x^56+1874x^57+2754x^58+3390x^59+1824x^60+1440x^61+1728x^62+258x^63+12x^64+24x^65+16x^66+12x^68+6x^69

The gray image is a linear code over GF(3) with n=261, k=9 and d=159.
This code was found by Heurico 1.16 in 0.333 seconds.