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  0  X  X  0  X  X  0
 0  0  X  0  0  0  0  0  0  0 2X  X  X  X 2X  0
 0  0  0  X  0  0  0  0  0  X 2X  0 2X  0 2X  X
 0  0  0  0  X  0  0  0  0 2X 2X  0 2X  X  0 2X
 0  0  0  0  0  X  0  0  0 2X 2X  X 2X 2X 2X 2X
 0  0  0  0  0  0  X  0  0 2X 2X 2X  X  0  0 2X
 0  0  0  0  0  0  0  X  0 2X  X 2X  0  X 2X 2X
 0  0  0  0  0  0  0  0  X 2X  0 2X 2X  X 2X  X

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+84x^15+270x^18+628x^21+1482x^24+2642x^27+3792x^30+39366x^32+4182x^33+3378x^36+2034x^39+894x^42+270x^45+26x^48

The gray image is a linear code over GF(3) with n=48, k=10 and d=15.
This code was found by Heurico 1.16 in 2.71 seconds.