The generator matrix

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

generates a code of length 10 over Z27 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+108x^14+144x^15+810x^16+648x^17+60x^18+3240x^19+10044x^20+240x^21+3240x^22+864x^23+180x^24+20x^27+24x^30

The gray image is a code over GF(3) with n=90, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0866 seconds.