The generator matrix

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

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+226x^21+612x^22+666x^23+1744x^24+2898x^25+3258x^26+6242x^27+10008x^28+11628x^29+16426x^30+21996x^31+19584x^32+21082x^33+21456x^34+14562x^35+11340x^36+7866x^37+2790x^38+1942x^39+774x^40+34x^42+12x^45

The gray image is a linear code over GF(3) with n=48, k=11 and d=21.
This code was found by Heurico 1.16 in 54.7 seconds.