The generator matrix
1 0 1 1 1 1 1
0 1 1 0 2X+1 X 2X+1
0 0 2X X X 2X 0
generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 11.
Homogenous weight enumerator: w(x)=1x^0+36x^11+28x^12+90x^14+48x^15+36x^17+2x^18+2x^21
The gray image is a linear code over GF(3) with n=21, k=5 and d=11.
This code was found by Heurico 1.16 in 0.000283 seconds.