The generator matrix
1 0 1 1 1 1 1 2X^2+X 1 1 1 0 2X
0 1 2X^2+2X+1 2 2X^2+X X+1 2X^2+X+2 1 2X 2X+2 2X^2+2X+1 X 1
0 0 2X^2 0 2X^2 X^2 X^2 X^2 0 0 X^2 2X^2 0
0 0 0 X^2 2X^2 2X^2 X^2 0 X^2 2X^2 0 0 2X^2
generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+96x^21+216x^22+1348x^24+864x^25+486x^26+2526x^27+864x^28+154x^30+2x^33+2x^36+2x^39
The gray image is a linear code over GF(3) with n=117, k=8 and d=63.
This code was found by Heurico 1.16 in 0.0204 seconds.