The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+24x^21+80x^24+328x^27+428x^30+776x^33+446x^36+80x^39+8x^42+8x^45+8x^48

The gray image is a linear code over GF(3) with n=48, k=7 and d=21.
This code was found by Heurico 1.16 in 0.0146 seconds.