The generator matrix

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

generates a code of length 29 over Z3[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+186x^49+162x^50+428x^51+1416x^52+1134x^53+1560x^54+5784x^55+6750x^56+3912x^57+10560x^58+11664x^59+4164x^60+7542x^61+2106x^62+762x^63+642x^64+54x^65+66x^66+108x^67+30x^69+6x^70+6x^72+4x^78+2x^81

The gray image is a linear code over GF(3) with n=261, k=10 and d=147.
This code was found by Heurico 1.16 in 13.2 seconds.