The generator matrix

 1  0  1  1  1  1  1  1 21  1  1 24 18  0  3  1
 0  1  1 26 18 17 21 25  1 19 20  1  1  1  9  3
 0  0 24  9 21 12 15  3  9 18  6  9 21 24  3  3

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

Homogenous weight enumerator: w(x)=1x^0+44x^27+264x^28+444x^29+786x^30+900x^31+1242x^32+1422x^33+918x^34+396x^35+90x^36+24x^37+24x^38+6x^39

The gray image is a code over GF(3) with n=144, k=8 and d=81.
This code was found by Heurico 1.16 in 0.0232 seconds.