The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+558x^51+180x^52+600x^54+288x^55+522x^57+18x^58+18x^60+2x^81

The gray image is a linear code over GF(3) with n=243, k=7 and d=153.
This code was found by Heurico 1.16 in 8.61 seconds.