The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2X+1 0 0
0 0 2X 0 0 0 0 0 0 2X X X 2X X 0 0 0
0 0 0 X 0 0 0 0 0 2X 2X 2X 2X 0 X 0 0
0 0 0 0 X 0 0 0 X 2X 2X 2X X X 0 X 0
0 0 0 0 0 2X 0 0 2X 2X 2X 0 2X X X X 0
0 0 0 0 0 0 X 0 X X 2X X 2X X 2X 0 0
0 0 0 0 0 0 0 X X X 0 0 2X 0 X 2X 0
generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+56x^18+224x^21+54x^22+392x^24+432x^25+1114x^27+2376x^28+3092x^30+8424x^31+5618x^33+15120x^34+5528x^36+11232x^37+2720x^39+1728x^40+566x^42+294x^45+66x^48+12x^51
The gray image is a linear code over GF(3) with n=51, k=10 and d=18.
This code was found by Heurico 1.16 in 2.8 seconds.