The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+80x^48+192x^51+1696x^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=243, k=7 and d=144.
This code was found by Heurico 1.16 in 1.94 seconds.