The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+654x^32+944x^33+1602x^34+3612x^35+7020x^36+5940x^37+13752x^38+13306x^39+5994x^40+4728x^41+1276x^42+72x^43+96x^44+48x^45+2x^48+2x^54

The gray image is a linear code over GF(3) with n=171, k=10 and d=96.
This code was found by Heurico 1.16 in 1.79 seconds.