The generator matrix
1 0 1 1 1 1 1 1
0 1 2X+4 8 X+3 X+1 8 0
0 0 3 0 0 6 6 0
0 0 0 6 0 3 6 6
0 0 0 0 3 3 0 3
generates a code of length 8 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+20x^9+18x^10+478x^12+108x^13+2106x^14+1792x^15+8964x^16+4212x^17+1788x^18+144x^19+44x^21+8x^24
The gray image is a code over GF(3) with n=72, k=9 and d=27.
This code was found by Heurico 1.16 in 0.0312 seconds.