The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+90x^49+112x^51+180x^52+74x^54+54x^55+126x^58+48x^60+36x^61+6x^63+2x^78

The gray image is a linear code over GF(3) with n=81, k=6 and d=49.
This code was found by Heurico 1.16 in 1.34 seconds.