The generator matrix

 1  0  0  1  1  1  1  1  1 15  1  1  1  1  1  1
 0  1  0 15  1 16 17  9 20  1  7  4 21  2 19 24
 0  0  1 16  1 15 20 17  6 16 14 26 23 10 21  8

generates a code of length 16 over Z27 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+118x^27+798x^28+1314x^29+2116x^30+2202x^31+4992x^32+3942x^33+2652x^34+1302x^35+214x^36+18x^37+6x^38+8x^39

The gray image is a code over GF(3) with n=144, k=9 and d=81.
This code was found by Heurico 1.16 in 0.155 seconds.