The generator matrix

 1  0  0  0  1  1  1  1  1 2X  1  1  X  X  1 2X
 0  1  0  0  1 2X 2X+1 2X+2 2X+1  0  X  1  1  1  X  1
 0  0  1  0  2 2X+1 X+1 2X+2 2X+2  1 X+2 X+1 2X+1 2X 2X+1 2X+1
 0  0  0  1  2 2X+2  1 2X+1  X 2X+1 2X X+2 X+2 2X 2X+1  X
 0  0  0  0 2X 2X 2X  X  0  X 2X  X  X 2X 2X 2X

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+550x^24+2344x^27+5118x^30+7258x^33+3944x^36+444x^39+22x^42+2x^45

The gray image is a linear code over GF(3) with n=48, k=9 and d=24.
This code was found by Heurico 1.16 in 17.5 seconds.