The generator matrix

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

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+918x^45+3588x^48+7812x^51+12896x^54+16716x^57+11814x^60+4500x^63+756x^66+30x^69+18x^72

The gray image is a linear code over GF(3) with n=84, k=10 and d=45.
This code was found by Heurico 1.16 in 23.5 seconds.