The generator matrix

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

generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+418x^81+1092x^84+1326x^87+1182x^90+1116x^93+804x^96+474x^99+108x^102+30x^105+4x^108+6x^111

The gray image is a linear code over GF(3) with n=135, k=8 and d=81.
This code was found by Heurico 1.16 in 0.606 seconds.