The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1  1 26 18 17 21  2 24  9
 0  0 24  9 21 12 15  3 15 21

generates a code of length 10 over Z27 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+40x^15+126x^16+150x^17+824x^18+312x^19+2940x^20+1578x^21+348x^22+150x^23+62x^24+24x^25+6x^27

The gray image is a code over GF(3) with n=90, k=8 and d=45.
This code was found by Heurico 1.16 in 0.0114 seconds.