The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+108x^28+108x^29+28x^30+72x^31+126x^32+48x^33+72x^34+72x^35+72x^37+18x^38+2x^39+2x^45

The gray image is a linear code over GF(3) with n=48, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0409 seconds.