The generator matrix

 1  0  1  1  1  1  1 18  1 24  1  0  1  1  1  1
 0  1  1 26  0 25 17  1 18  1 25  1 14  3 16  0
 0  0 24  0  9  3 21  3 21  6 12 21  3 12 15  9
 0  0  0  3 15  9 15 15  9  0  6 21 18 24 15  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+102x^25+330x^26+752x^27+1356x^28+1722x^29+8592x^30+5994x^31+14562x^32+16260x^33+5424x^34+2298x^35+1200x^36+228x^37+42x^38+84x^39+18x^40

The gray image is a code over GF(3) with n=144, k=10 and d=72.
This code was found by Heurico 1.16 in 1.51 seconds.