The generator matrix
1 1 1 1 1 1 1 1 1 X
0 6 0 0 0 6 0 3 3 6
0 0 6 0 0 3 6 0 3 3
0 0 0 6 0 3 6 3 0 6
0 0 0 0 6 6 6 6 3 0
generates a code of length 10 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+72x^15+222x^18+1458x^20+324x^21+90x^24+20x^27
The gray image is a code over GF(3) with n=90, k=7 and d=45.
This code was found by Heurico 1.16 in 0.00307 seconds.