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.