The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+12x^37+54x^38+4x^39+6x^40+2x^42+2x^51

The gray image is a linear code over GF(3) with n=171, k=4 and d=111.
This code was found by Heurico 1.16 in 0.00101 seconds.