The generator matrix
1 0 1 1 1 1
0 1 2X+4 0 0 0
0 0 3 0 0 0
0 0 0 6 0 0
0 0 0 0 6 0
0 0 0 0 0 6
generates a code of length 6 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+12x^3+72x^4+60x^6+576x^7+160x^9+5616x^10+41064x^12+10080x^13+192x^15+1152x^16+64x^18
The gray image is a code over GF(3) with n=54, k=10 and d=9.
This code was found by Heurico 1.16 in 0.0972 seconds.