The generator matrix

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

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+190x^48+138x^49+192x^50+262x^51+780x^52+384x^53+2302x^54+1362x^55+288x^56+192x^57+60x^58+96x^59+176x^60+84x^61+12x^62+34x^63+6x^64+2x^75

The gray image is a linear code over GF(3) with n=243, k=8 and d=144.
This code was found by Heurico 1.16 in 0.298 seconds.