The generator matrix
1 1 1 1 1 1 1 1
0 6 0 0 6 0 6 6
0 0 6 0 3 6 3 6
0 0 0 6 3 3 0 3
generates a code of length 8 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+20x^12+32x^15+648x^16+8x^18+16x^21+4x^24
The gray image is a code over GF(3) with n=72, k=6 and d=36.
This code was found by Heurico 1.16 in 0.000419 seconds.