The generator matrix
1 0 1 1 1 1 1
0 1 1 2 0 0 0
0 0 2X 0 0 0 X
0 0 0 X 0 0 X
0 0 0 0 X 0 X
0 0 0 0 0 X 2X
generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+60x^6+214x^9+2100x^12+3702x^15+442x^18+42x^21
The gray image is a linear code over GF(3) with n=21, k=8 and d=6.
This code was found by Heurico 1.16 in 0.00551 seconds.