The generator matrix

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

generates a code of length 16 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+84x^24+18x^26+146x^27+54x^28+108x^29+1278x^30+216x^31+1674x^32+2292x^33+216x^34+144x^35+222x^36+90x^39+18x^42

The gray image is a code over GF(3) with n=144, k=8 and d=72.
This code was found by Heurico 1.16 in 0.0412 seconds.