The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X 0 X^2
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2 X 2X^2+2X 2X^2+X 2X X^2+X X^2+2X X X
generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 47.
Homogenous weight enumerator: w(x)=1x^0+108x^47+72x^48+54x^50+8x^54
The gray image is a linear code over GF(3) with n=216, k=5 and d=141.
This code was found by Heurico 1.16 in 0.0024 seconds.