The generator matrix
1 1 1 1 1 1 1
0 X 0 0 0 X 0
0 0 X 0 0 2X 0
0 0 0 X 0 2X 0
0 0 0 0 X X 0
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+20x^6+30x^9+50x^12+486x^14+70x^15+50x^18+22x^21
The gray image is a linear code over GF(3) with n=21, k=6 and d=6.
This code was found by Heurico 1.16 in 0.000232 seconds.