The generator matrix

 1  0  0  1  1  1  1  1  0  0  0  0  X  1  1  1
 0  1  0  1  0  2  1  2  1  1  1  1  1  0  1  0
 0  0  1  2  1  2  1  0  2  0  0  X 2X+2 X+2 X+1  0
 0  0  0 2X  0  0  0  X  X  X  X 2X 2X  X 2X  0
 0  0  0  0 2X  0 2X 2X  X  X  0  X  0  0 2X  X
 0  0  0  0  0  X  X  X  0  X 2X  X  X  0  X  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+46x^21+30x^22+30x^23+392x^24+192x^25+228x^26+1126x^27+660x^28+948x^29+2924x^30+1428x^31+1806x^32+4028x^33+1536x^34+1230x^35+1970x^36+528x^37+132x^38+428x^39+8x^42+8x^45+4x^48

The gray image is a linear code over GF(3) with n=48, k=9 and d=21.
This code was found by Heurico 1.16 in 0.587 seconds.