The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  3 24  0 21 24  0  9 21 21
 0  0  9  0  9  0 18 18 18 18
 0  0  0  9 18  9  9 18  9 18

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

Homogenous weight enumerator: w(x)=1x^0+54x^15+18x^16+118x^18+72x^19+1620x^20+146x^21+72x^22+78x^24+4x^27+4x^30

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 0.00291 seconds.