The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 1 1
0 X 0 0 0 0 X 2X 2X 0 X 0 X X 2X
0 0 X 0 0 X 2X 0 2X 0 X X 2X 0 2X
0 0 0 X 0 2X 2X X 0 X X 2X X 2X X
0 0 0 0 X 2X 2X 2X 2X 2X 2X 0 0 2X 2X
generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+60x^24+40x^27+162x^28+62x^30+324x^31+20x^33+40x^36+10x^39+10x^42
The gray image is a linear code over GF(3) with n=45, k=6 and d=24.
This code was found by Heurico 1.16 in 0.0225 seconds.