The generator matrix
1 1 1 1
0 6 0 0
0 0 6 0
0 0 0 6
generates a code of length 4 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+8x^3+24x^6+648x^8+32x^9+16x^12
The gray image is a code over GF(3) with n=36, k=6 and d=9.
This code was found by Heurico 1.16 in 9.7e-005 seconds.