The generator matrix

 1  0  0  0  0  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  0  1 2X+1  2  2 2X+2  1  1  X
 0  0  1  0  0  1  2 2X+1  0 X+2 X+2 2X 2X+2 2X
 0  0  0  1  0  2  2 2X+1 X+1 2X 2X X+2 X+2 X+1
 0  0  0  0  1  2 X+1 2X 2X+1 2X+2  1  2  0 2X+1
 0  0  0  0  0 2X  X  0  X  0 2X  0 2X 2X

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+162x^17+142x^18+972x^19+1548x^20+636x^21+4500x^22+7830x^23+2852x^24+17640x^25+22536x^26+7062x^27+29916x^28+30798x^29+7068x^30+21852x^31+14472x^32+1736x^33+3852x^34+1386x^35+166x^36+18x^39+2x^42

The gray image is a linear code over GF(3) with n=42, k=11 and d=17.
This code was found by Heurico 1.16 in 42.2 seconds.