The generator matrix
1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 X
0 0 X 0 0 2X X 2X
0 0 0 X 0 2X X X
0 0 0 0 X X X X
generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+20x^9+46x^12+64x^15+486x^16+60x^18+44x^21+8x^24
The gray image is a linear code over GF(3) with n=24, k=6 and d=9.
This code was found by Heurico 1.16 in 0.000573 seconds.