The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+56x^24+84x^26+110x^27+348x^29+150x^30+558x^32+182x^33+420x^35+168x^36+48x^38+48x^39+14x^42

The gray image is a linear code over GF(3) with n=48, k=7 and d=24.
This code was found by Heurico 1.16 in 0.0117 seconds.