The generator matrix

 1  0  1  1  1  1 21  1  1  1 18  1  3 18  3  1
 0  1  1 26 18 17  1 16 20 16  1 25  1  3 24  1
 0  0 24  0 21 21 18 15  6  9 21 12 12 21 24  3
 0  0  0  9 18  9 18  9  0  0 18  9  0  0 18 18

generates a code of length 16 over Z27 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+276x^26+118x^27+738x^28+1578x^29+1488x^30+2484x^31+5328x^32+2844x^33+2538x^34+1974x^35+140x^36+72x^37+78x^38+24x^39+2x^45

The gray image is a code over GF(3) with n=144, k=9 and d=78.
This code was found by Heurico 1.16 in 0.202 seconds.