The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+80x^48+192x^51+238x^54+166x^57+12x^60+2x^63+22x^66+12x^69+2x^72+2x^75

The gray image is a linear code over GF(3) with n=81, k=6 and d=48.
This code was found by Heurico 1.16 in 0.866 seconds.