The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+180x^46+372x^47+770x^48+1386x^49+2298x^50+3562x^51+5760x^52+7428x^53+11522x^54+10440x^55+7668x^56+4516x^57+1908x^58+582x^59+248x^60+234x^61+114x^62+36x^63+18x^64+6x^65

The gray image is a linear code over GF(3) with n=243, k=10 and d=138.
This code was found by Heurico 1.16 in 4.48 seconds.