The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 1 1 1 0 X
0 1 1 2 2X+1 0 2 1 X 2X+1 X+2 1 X X+1 X+2 1 X+1 0 X 1 2 X+2 1 1
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X X 2X 0 0 X 0 X 2X
generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.
Homogenous weight enumerator: w(x)=1x^0+66x^45+126x^48+18x^51+32x^54
The gray image is a linear code over GF(3) with n=72, k=5 and d=45.
This code was found by Heurico 1.16 in 0.00199 seconds.