The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  X  X  X  X  0 2X  0  0
 0  0  X  0  0  0  0  X 2X  X 2X  X  X  X  0  0
 0  0  0  X  0  0  0 2X 2X  0  X  X  0  X  0  0
 0  0  0  0  X  0  0 2X 2X  X  0 2X  0 2X  0  0
 0  0  0  0  0  X  0 2X 2X 2X  0  0  X  X  0  0
 0  0  0  0  0  0  X 2X  X  X 2X  0  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+132x^18+44x^21+174x^24+308x^27+1698x^30+3486x^33+252x^36+198x^39+228x^42+36x^45+4x^48

The gray image is a linear code over GF(3) with n=48, k=8 and d=18.
This code was found by Heurico 1.16 in 0.073 seconds.