The generator matrix
1 0 0 1 1 1 1 1
0 1 0 1 2X+6 8 7 0
0 0 1 8 2X+7 8 7 X
0 0 0 2X 2X+6 3 X+6 X+3
generates a code of length 8 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+306x^10+264x^11+3118x^12+1836x^13+23454x^14+12408x^15+73656x^16+46908x^17+12404x^18+2448x^19+330x^20+8x^21+6x^24
The gray image is a code over GF(3) with n=72, k=11 and d=30.
This code was found by Heurico 1.16 in 2.52 seconds.