The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+514x^48+1296x^49+2382x^50+4034x^51+9030x^52+9144x^53+18076x^54+25650x^55+24792x^56+32556x^57+25950x^58+12660x^59+6550x^60+3516x^61+540x^62+202x^63+162x^64+48x^65+32x^66+6x^67+6x^68

The gray image is a linear code over GF(3) with n=252, k=11 and d=144.
This code was found by Heurico 1.16 in 144 seconds.