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

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+180x^46+246x^47+306x^48+336x^49+480x^50+348x^51+600x^52+588x^53+376x^54+570x^55+606x^56+424x^57+510x^58+366x^59+186x^60+210x^61+132x^62+58x^63+24x^64+12x^65+2x^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 0.196 seconds.