The generator matrix

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

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+390x^81+1116x^84+1350x^87+1234x^90+1002x^93+858x^96+412x^99+168x^102+24x^105+6x^108

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 0.421 seconds.