The generator matrix
1 0 0 0 0 1 1 1 1
0 1 0 0 0 1 0 1 X
0 0 1 0 0 2 1 2 X
0 0 0 1 0 2 2 1 0
0 0 0 0 1 2 X+1 0 X
0 0 0 0 0 2X X X 2X
generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+90x^8+234x^9+486x^10+900x^11+1818x^12+3888x^13+8460x^14+8982x^15+20412x^16+26640x^17+22452x^18+33048x^19+26640x^20+11574x^21+7776x^22+2880x^23+846x^24+20x^27
The gray image is a linear code over GF(3) with n=27, k=11 and d=8.
This code was found by Heurico 1.16 in 13.7 seconds.