The generator matrix
1 1 1 1 1 1 1 1
0 X 0 0 X 0 X X
0 0 X 0 2X X 2X X
0 0 0 X 2X 2X 0 2X
generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+20x^12+32x^15+162x^16+8x^18+16x^21+4x^24
The gray image is a linear code over GF(3) with n=24, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000281 seconds.