The generator matrix
1 1 1 1 1 1
0 X 0 0 X 0
0 0 X 0 2X 0
0 0 0 X 2X 0
generates a code of length 6 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+12x^6+16x^9+180x^12+24x^15+10x^18
The gray image is a linear code over GF(3) with n=18, k=5 and d=6.
This code was found by Heurico 1.16 in 0.000107 seconds.