The generator matrix

 1  0  0  0  1  1  1 24  1  1  1  9
 0  1  0  0 15 19 16  1 24  4 11  1
 0  0  1  0 16 19 14 25 15 24  1 21
 0  0  0  1 14 21 17  2 22  9 19  7

generates a code of length 12 over Z27 who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+96x^17+2728x^18+1914x^19+13698x^20+12844x^21+73260x^22+54180x^23+153574x^24+143226x^25+54282x^26+18106x^27+3216x^28+216x^29+98x^30+2x^33

The gray image is a code over GF(3) with n=108, k=12 and d=51.
This code was found by Heurico 1.16 in 53.8 seconds.