The generator matrix

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

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+1002x^45+4854x^48+13242x^51+29148x^54+44914x^57+46078x^60+28114x^63+8326x^66+1372x^69+82x^72+10x^75+4x^78

The gray image is a linear code over GF(3) with n=87, k=11 and d=45.
This code was found by Heurico 1.16 in 276 seconds.