The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  0  1  1  1  1  X  1  1 2X  1  0  X 2X  X  0
 0  1  1  2  0 2X+1  2  1  2  0 2X+1  1  1 2X+1  0 2X+1  1  1  2 X+2  1 2X+2  1  1  1  X  1
 0  0 2X  0  0 2X  0  X  X  0  X  0  0  X 2X  X  X 2X 2X 2X 2X  X 2X 2X  0  X  0
 0  0  0  X  0 2X 2X 2X 2X  X  X  0  X  0  0  X  0 2X  X  X  X 2X  0  0 2X  X  0
 0  0  0  0  X  X  X  0 2X 2X 2X  X  X  0  X  0  X 2X  0 2X  X  X  X 2X  0  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+42x^46+162x^47+64x^48+162x^49+84x^50+84x^51+192x^52+240x^53+20x^54+300x^55+288x^56+18x^57+234x^58+150x^59+12x^60+42x^61+48x^62+6x^63+24x^66+12x^69+2x^75

The gray image is a linear code over GF(3) with n=81, k=7 and d=46.
This code was found by Heurico 1.16 in 1.56 seconds.