The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+156x^46+330x^47+370x^48+726x^49+960x^50+804x^51+1128x^52+1356x^53+1050x^54+1722x^55+1746x^56+1212x^57+1920x^58+1716x^59+1330x^60+1392x^61+1002x^62+304x^63+210x^64+174x^65+12x^66+36x^67+6x^68+4x^69+4x^72+8x^75+4x^78

The gray image is a linear code over GF(3) with n=84, k=9 and d=46.
This code was found by Heurico 1.16 in 1.88 seconds.