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 X X X X 0 0 0 0 1 1 1 1 1 1
0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 X X 0 X 2X 2X 2X X X X 0 0 0 X X 0 X
0 0 X 2X 2X X 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 0 0 X 2X X 2X X 2X 0 0 X 2X 0 X 2X X 0 X 2X X 2X 2X
generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.
Homogenous weight enumerator: w(x)=1x^0+64x^90+6x^93+6x^96+4x^99
The gray image is a linear code over GF(3) with n=135, k=4 and d=90.
As d=90 is an upper bound for linear (135,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0103 seconds.