The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+576x^26+406x^27+3708x^28+6252x^29+16984x^30+20748x^31+69810x^32+65522x^33+110826x^34+131022x^35+65464x^36+27864x^37+10938x^38+1050x^39+150x^40+102x^41+16x^42+2x^48

The gray image is a linear code over GF(3) with n=153, k=12 and d=78.
This code was found by Heurico 1.16 in 93.8 seconds.