The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1  X  1  1
 0  X  0  0  0  0  0  0  0  0  X  X  X 2X  X 2X  X 2X  X  X  X 2X  X  0  0  X  X  0
 0  0  X  0  0  0  0  X 2X 2X 2X  X  X  0 2X  X  X  0  X 2X  X  0  0 2X 2X  0 2X  0
 0  0  0  X  0  0  X 2X  0 2X  0  X 2X  0 2X 2X  X 2X 2X  0  X  0 2X  X  0  X  0  0
 0  0  0  0  X  0 2X 2X  X  0 2X  X  X  0  X  0  X 2X 2X  0 2X  X  0  0 2X  0 2X 2X
 0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  0  X 2X 2X  0  0  X  X  0 2X  X 2X  X  0  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+60x^45+110x^48+262x^51+534x^54+660x^57+376x^60+82x^63+54x^66+28x^69+16x^72+4x^75

The gray image is a linear code over GF(3) with n=84, k=7 and d=45.
This code was found by Heurico 1.16 in 0.067 seconds.