The generator matrix
1 0 1 1 1 1 1 1 1
0 1 1 2 0 1 2 0 0
0 0 2X 0 0 0 X 0 X
0 0 0 X 0 0 2X 0 X
0 0 0 0 X 0 X X 0
0 0 0 0 0 2X 2X 2X X
generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+32x^9+18x^10+78x^12+144x^13+324x^14+138x^15+918x^16+1296x^17+212x^18+1548x^19+1296x^20+156x^21+288x^22+96x^24+16x^27
The gray image is a linear code over GF(3) with n=27, k=8 and d=9.
This code was found by Heurico 1.16 in 0.00938 seconds.