The generator matrix

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

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+126x^32+116x^33+432x^35+698x^36+3294x^38+1220x^39+360x^41+100x^42+162x^44+46x^45+4x^48+2x^54

The gray image is a linear code over GF(3) with n=171, k=8 and d=96.
This code was found by Heurico 1.16 in 0.115 seconds.