The generator matrix

 1  0  0  0  1  1  1  1  1 2X  1  1  1  0  1  1
 0  1  0  0  0  1 2X+1 2X+2  2  1 2X 2X 2X  X  2 2X
 0  0  1  0  1  2 2X+1 2X  2 2X+2 2X 2X+1  2 2X 2X+2 2X
 0  0  0  1  2  2 2X+1 2X+1  0 2X+1 X+1  X  0  1  1 2X+1
 0  0  0  0 2X  0  X 2X  X 2X  0  0 2X  X  X 2X
 0  0  0  0  0 2X  X  X 2X  0  X 2X  0  0  0  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+138x^21+96x^22+294x^23+734x^24+666x^25+1140x^26+2578x^27+2574x^28+3876x^29+6490x^30+6180x^31+6258x^32+8486x^33+6030x^34+4854x^35+4916x^36+1854x^37+1038x^38+676x^39+96x^40+36x^41+32x^42+2x^45+4x^48

The gray image is a linear code over GF(3) with n=48, k=10 and d=21.
This code was found by Heurico 1.16 in 4.86 seconds.