The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3
 0  3  0  9 24 21 21 15 24  0 18  3  3 24 15 15
 0  0  3 15  9  6  3 21 24  9 24 18 15  0 15 12

generates a code of length 16 over Z27 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+108x^28+114x^29+190x^30+72x^31+1080x^32+372x^33+72x^34+90x^35+72x^37+12x^38+2x^39+2x^45

The gray image is a code over GF(3) with n=144, k=7 and d=84.
This code was found by Heurico 1.16 in 0.033 seconds.