The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+420x^27+1476x^28+666x^29+8070x^30+7020x^31+16416x^32+29928x^33+39852x^34+31266x^35+29728x^36+9972x^37+1224x^38+1056x^39+42x^42+10x^45

The gray image is a linear code over GF(3) with n=153, k=11 and d=81.
This code was found by Heurico 1.16 in 12.6 seconds.