The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0 2X 2X+1  1
 0  0  1  0 2X+1 2X+2  1
 0  0  0  1 2X+2 X+2  X

generates a code of length 7 over Z3[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+66x^8+156x^9+270x^10+396x^11+454x^12+1080x^13+1440x^14+894x^15+1080x^16+528x^17+188x^18+8x^21

The gray image is a linear code over GF(3) with n=21, k=8 and d=8.
This code was found by Heurico 1.16 in 0.031 seconds.