The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2X^2+2X  1  1 2X^2+X  1  1 2X^2  1 X^2  X  1  1 2X  1  1 2X^2+2X
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1 X+2 2X^2+2  1  2  1 2X^2+1 2X  1 2X^2+X+2  X  1 X+1  1  1 X^2+2X 2X^2  1 2X^2+1 X^2+X+1 X^2+X
 0  0  1 2X^2+2X+1 2X^2+2 2X^2+2X 2X^2+2X+2 2X+1 2X^2+X+2  1 2X X^2+2X+1 2X^2+2X+2 X^2+2 2X^2+2X X^2+2 2X^2+2X+1 2X^2+X+2 X+1 2X+1 X^2+1 X+2  1 X+2 X^2+X+1 X^2  1
 0  0  0 2X^2 2X^2  0 2X^2 X^2 X^2 2X^2 2X^2  0 X^2 2X^2 X^2  0  0 X^2 X^2  0 2X^2  0  0 X^2  0 2X^2 2X^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+926x^48+1566x^49+3582x^50+3240x^51+6642x^52+7128x^53+7886x^54+11178x^55+9018x^56+4394x^57+2484x^58+684x^59+252x^60+60x^63+8x^66

The gray image is a linear code over GF(3) with n=243, k=10 and d=144.
This code was found by Heurico 1.16 in 45 seconds.