The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+24x^51+90x^52+26x^54+54x^55+18x^57+12x^60+18x^61

The gray image is a linear code over GF(3) with n=81, k=5 and d=51.
This code was found by Heurico 1.13 in 0.00303 seconds.