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 1 1 1 1
0 X 0 0 X 0 X X 2X 0 0 X X 0 2X X 2X 2X 0 X 2X 0 X 2X 2X 2X 2X 0 0 0 X X 0 X X 2X 0 0 X X 2X 2X 2X 0 X
0 0 X 0 2X X 2X X 2X 0 X X 0 2X 0 0 X X 2X 2X 2X 2X X 0 0 X 2X 0 0 X 2X X X 2X 0 2X 0 X X 0 0 0 X 2X X
0 0 0 X 2X 2X 0 2X 2X 2X X 0 2X 0 2X X X 0 X X X 2X X 0 X 2X 0 0 X 2X 2X 2X X X X 2X 2X 0 0 0 0 2X 0 X X
generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.
Homogenous weight enumerator: w(x)=1x^0+36x^87+186x^90+18x^96+2x^135
The gray image is a linear code over GF(3) with n=135, k=5 and d=87.
This code was found by Heurico 1.16 in 0.0126 seconds.