The generator matrix

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

generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+138x^22+108x^23+586x^24+1398x^25+1296x^26+2748x^27+4590x^28+5364x^29+9410x^30+14538x^31+15156x^32+18970x^33+22296x^34+19062x^35+19108x^36+17172x^37+10296x^38+7466x^39+5142x^40+1206x^41+730x^42+336x^43+22x^45+8x^48

The gray image is a linear code over GF(3) with n=51, k=11 and d=22.
This code was found by Heurico 1.16 in 59.1 seconds.