The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+248x^51+330x^54+972x^56+588x^57+1458x^58+1944x^59+636x^60+282x^63+60x^66+30x^69+6x^72+4x^78+2x^81

The gray image is a linear code over GF(3) with n=261, k=8 and d=153.
This code was found by Heurico 1.16 in 0.284 seconds.