The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+118x^45+168x^46+222x^47+684x^48+384x^49+468x^50+1364x^51+624x^52+828x^53+2630x^54+1080x^55+1122x^56+2970x^57+1206x^58+1152x^59+2294x^60+618x^61+468x^62+738x^63+264x^64+114x^65+84x^66+30x^67+32x^69+14x^72+6x^75

The gray image is a linear code over GF(3) with n=84, k=9 and d=45.
This code was found by Heurico 1.16 in 1.89 seconds.