The generator matrix
1 0 1 1 1 1
0 1 1 0 0 0
0 0 2X 0 0 0
0 0 0 X 0 0
0 0 0 0 X 0
0 0 0 0 0 X
generates a code of length 6 over Z3[X]/(X^2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+12x^3+18x^4+60x^6+144x^7+160x^9+1404x^10+1698x^12+2520x^13+192x^15+288x^16+64x^18
The gray image is a linear code over GF(3) with n=18, k=8 and d=3.
This code was found by Heurico 1.16 in 0.0032 seconds.