The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+174x^46+300x^47+124x^48+504x^49+588x^50+162x^51+624x^52+654x^53+170x^54+774x^55+732x^56+142x^57+540x^58+510x^59+108x^60+258x^61+120x^62+18x^63+42x^64+12x^65+4x^66

The gray image is a linear code over GF(3) with n=81, k=8 and d=46.
This code was found by Heurico 1.16 in 0.219 seconds.