The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+330x^47+934x^48+4596x^49+7110x^50+11946x^51+24810x^52+30540x^53+56470x^54+73290x^55+75336x^56+94988x^57+75888x^58+41628x^59+20790x^60+10290x^61+1986x^62+250x^63+168x^64+42x^65+30x^66+12x^67+6x^68

The gray image is a linear code over GF(3) with n=252, k=12 and d=141.
This code was found by Heurico 1.16 in 189 seconds.