The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+78x^45+162x^46+120x^47+320x^48+486x^49+264x^50+432x^51+648x^52+390x^53+510x^54+774x^55+420x^56+492x^57+594x^58+222x^59+262x^60+216x^61+42x^62+68x^63+36x^64+16x^66+8x^69

The gray image is a linear code over GF(3) with n=81, k=8 and d=45.
This code was found by Heurico 1.16 in 0.192 seconds.