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

generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+78x^87+162x^88+22x^90+324x^91+14x^93+18x^96+4x^99+26x^102+10x^105+2x^132

The gray image is a linear code over GF(3) with n=135, k=6 and d=84.
This code was found by Heurico 1.16 in 38.4 seconds.