The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+242x^21+624x^22+570x^23+1678x^24+3096x^25+3126x^26+6432x^27+10278x^28+11496x^29+15998x^30+21288x^31+20274x^32+21652x^33+21258x^34+14586x^35+10954x^36+8244x^37+2436x^38+2048x^39+822x^40+34x^42+10x^45

The gray image is a linear code over GF(3) with n=48, k=11 and d=21.
This code was found by Heurico 1.16 in 40.8 seconds.