The generator matrix
1 0 1
0 1 2X+1
0 0 2X
generates a code of length 3 over Z3[X]/(X^2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+6x^3+54x^4+66x^6+108x^7+8x^9
The gray image is a linear code over GF(3) with n=9, k=5 and d=3.
This code was found by Heurico 1.16 in 5.32e-005 seconds.