The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+122x^18+210x^21+108x^22+540x^24+1080x^25+972x^26+842x^27+4320x^28+5832x^29+1194x^30+8640x^31+11664x^32+1440x^33+8640x^34+7776x^35+1140x^36+3456x^37+690x^39+288x^42+82x^45+12x^48

The gray image is a linear code over GF(3) with n=48, k=10 and d=18.
This code was found by Heurico 1.16 in 2.83 seconds.