The generator matrix

 1  0  0  0  1  1  1  1  1 2X  1  0  1  X  0  1
 0  1  0  0  1 2X 2X+1 2X+2 2X+1  0  X  1 X+2  1  1  X
 0  0  1  0  2 2X+1 X+1 2X+2 2X+2  1  2 X+2  1  X 2X+1  0
 0  0  0  1  2 2X+2  1 2X+1  X 2X+1  1 2X+1 X+1 X+2 2X+1 X+1
 0  0  0  0 2X 2X 2X  X  0  X  0 2X  0  X  0 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+244x^24+240x^25+576x^26+1484x^27+792x^28+576x^29+2664x^30+1200x^31+1782x^32+4024x^33+1560x^34+1152x^35+2340x^36+576x^37+288x^38+156x^39+6x^40+16x^42+6x^48

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 1.34 seconds.