The generator matrix

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

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+136x^18+238x^21+390x^24+890x^27+1422x^30+13122x^32+1272x^33+1074x^36+762x^39+282x^42+86x^45+8x^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 0.605 seconds.