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 X X X X 0 X^2 X X 2X^2 1 1 1 1 1 1 1 1 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2 X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2 X 2X^2+2X 2X^2+X 2X X^2+X X^2+2X X X X 2X^2+2X X 0 X^2 2X^2 2X^2+X X^2+X X 0 X^2 2X^2
generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.
Homogenous weight enumerator: w(x)=1x^0+236x^90+2x^99+4x^108
The gray image is a linear code over GF(3) with n=405, k=5 and d=270.
This code was found by Heurico 1.16 in 0.0215 seconds.