The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  X  1  1  1
 0  1  1  2  0  1  2  1  0 2X+1  2  1  0 2X+1  0  0
 0  0 2X  0  0  0  0  0  X 2X 2X 2X  X  0  0  0
 0  0  0  X  0  0  0  X 2X 2X  X 2X  0  0  0  0
 0  0  0  0  X  0  0 2X 2X  0 2X 2X 2X  0  0  0
 0  0  0  0  0 2X  0 2X 2X  X 2X  X  X 2X  X  0
 0  0  0  0  0  0  X  X  X  X  0 2X  X 2X 2X  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+44x^18+18x^20+130x^21+18x^22+144x^23+264x^24+180x^25+468x^26+1064x^27+720x^28+864x^29+3036x^30+1440x^31+1152x^32+3954x^33+1440x^34+1152x^35+2028x^36+576x^37+576x^38+234x^39+156x^42+22x^45+2x^48

The gray image is a linear code over GF(3) with n=48, k=9 and d=18.
This code was found by Heurico 1.16 in 0.429 seconds.