The generator matrix

 1  1  1  1  1  1  3  1  1  1
 0  3  0 21 24  9 21  9 12  9
 0  0  3 15 18 15 24 24 15 18

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

Homogenous weight enumerator: w(x)=1x^0+16x^15+36x^16+42x^17+320x^18+60x^19+1050x^20+498x^21+42x^22+42x^23+50x^24+24x^25+6x^27

The gray image is a code over GF(3) with n=90, k=7 and d=45.
This code was found by Heurico 1.16 in 0.00271 seconds.