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.