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.