The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^26+204x^27+252x^28+96x^29+1162x^30+540x^31+1170x^32+1960x^33+594x^34+144x^35+272x^36+72x^37+12x^38+44x^39+2x^42

The gray image is a code over GF(3) with n=144, k=8 and d=78.
This code was found by Heurico 1.16 in 0.0473 seconds.