The generator matrix

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

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+266x^81+54x^84+324x^87+908x^90+432x^93+136x^99+60x^108+4x^117+2x^126

The gray image is a linear code over GF(3) with n=135, k=7 and d=81.
This code was found by Heurico 1.16 in 39.5 seconds.