The generator matrix
1 1 1 1 1 1 1 1 1 X
0 X 0 0 0 X 0 2X 2X X
0 0 X 0 0 2X X 0 2X 2X
0 0 0 X 0 2X X 2X 0 X
0 0 0 0 X X X X 2X 0
generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+72x^15+222x^18+324x^21+90x^24+20x^27
The gray image is a linear code over GF(3) with n=30, k=6 and d=15.
This code was found by Heurico 1.16 in 0.00105 seconds.