The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  X  1  1  1  1
 0  1  1  2  0  1  2  1  0  0  0  X 2X+1 2X+1  X  0
 0  0 2X  0  0  0  0  X  X  X 2X 2X 2X 2X 2X  0
 0  0  0  X  0  0  X 2X 2X  0 2X 2X  X 2X 2X  0
 0  0  0  0  X  0 2X 2X  X 2X  0 2X  X 2X  X  0
 0  0  0  0  0 2X  X 2X  X  X  X  0  X  0  X  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+26x^21+42x^22+76x^24+138x^25+108x^26+114x^27+534x^28+648x^29+100x^30+828x^31+1296x^32+136x^33+888x^34+864x^35+172x^36+438x^37+82x^39+48x^40+4x^42+10x^45+8x^48

The gray image is a linear code over GF(3) with n=48, k=8 and d=21.
This code was found by Heurico 1.16 in 0.073 seconds.