The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1
0 1 1 2 0 1 2 1 0 0 0 X X
0 0 2X 0 0 0 0 X X X 2X 2X 2X
0 0 0 X 0 0 X 2X 2X 0 2X 2X 2X
0 0 0 0 X 0 2X 2X X 2X 0 2X X
0 0 0 0 0 2X X 2X X X X 0 X
generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+174x^18+162x^20+324x^21+972x^23+414x^24+1944x^26+548x^27+1296x^29+630x^30+72x^33+6x^36+18x^39
The gray image is a linear code over GF(3) with n=39, k=8 and d=18.
This code was found by Heurico 1.16 in 0.0531 seconds.