The generator matrix

 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  0  0 2X^2  X 2X^2+X  X 2X^2 2X^2+X 2X^2+2X X^2+2X  0 2X^2+X  X X^2+2X 2X^2+2X 2X 2X^2 2X^2 X^2+X X^2+2X 2X^2+2X X^2+2X  0 2X^2 2X^2+X
 0  0  X  0 2X^2+X 2X 2X X^2 2X X^2+X  X X^2+2X X^2  0 2X^2+X X^2 2X^2+X 2X^2 2X^2+X 2X^2+2X X^2+X 2X^2 2X  X X^2+2X  0  0
 0  0  0  X 2X^2+2X X^2+X X^2+2X 2X^2+X 2X^2 2X^2+X  X X^2 2X^2+2X 2X^2+2X 2X^2 2X^2+X X^2  0 2X X^2+X 2X X^2+2X 2X^2+X 2X 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+162x^46+300x^47+272x^48+390x^49+606x^50+360x^51+2478x^52+1158x^53+6220x^54+4494x^55+1320x^56+476x^57+528x^58+348x^59+174x^60+168x^61+138x^62+28x^63+42x^64+18x^65+2x^75

The gray image is a linear code over GF(3) with n=243, k=9 and d=138.
This code was found by Heurico 1.16 in 0.667 seconds.