The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 1
0 X 0 0 2X^2 X 2X^2+X X 2X^2 2X^2+X 2X^2+2X 0 2X 2X^2+X
0 0 X 0 2X^2+X 2X 2X X^2 2X X^2+X X X^2 0 2X
0 0 0 X 2X^2+2X X^2+X X^2+2X 2X^2+X 2X^2 2X^2+X X 2X^2+2X 2X^2 X^2
generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+92x^21+234x^22+240x^23+470x^24+366x^25+1968x^26+854x^27+9378x^28+3780x^29+972x^30+594x^31+318x^32+274x^33+120x^34+12x^35+6x^36+4x^39
The gray image is a linear code over GF(3) with n=126, k=9 and d=63.
This code was found by Heurico 1.16 in 0.266 seconds.