The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+330x^19+588x^20+576x^21+1410x^22+2136x^23+1946x^24+4560x^25+6204x^26+5906x^27+8580x^28+8376x^29+5592x^30+5610x^31+4182x^32+1256x^33+1380x^34+384x^35+24x^36+6x^39+2x^42

The gray image is a linear code over GF(3) with n=42, k=10 and d=19.
This code was found by Heurico 1.16 in 350 seconds.