The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  1  2  2  1  2  2  2  2  4  4  2  1
 0 12  0  0  0  4 12  4  0  8  0  4  4  4 12  0 12  8  0  4  8  4  0 12  8 12  0
 0  0 12  0  4  4 12  0  0  0  4 12  8  4  8  4  4  4 12  4  8  8  8  4 12 12  0
 0  0  0 12  4  0 12  4  0  4  4  4 12  0  8  4 12  0  4  0 12  4  4  4 12  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  8  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  0  8  8  0  8  0  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  0  8  8  8  0  0  8  8  0  8  0
 0  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  8  8  8  0  0  0  8  0  0  8  0

generates a code of length 27 over Z16 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+48x^18+86x^19+224x^20+314x^21+628x^22+762x^23+1243x^24+2740x^25+5981x^26+8536x^27+6104x^28+2808x^29+1344x^30+784x^31+569x^32+268x^33+170x^34+66x^35+48x^36+14x^37+20x^38+6x^39+3x^40+1x^42

The gray image is a code over GF(2) with n=216, k=15 and d=72.
This code was found by Heurico 1.16 in 6.23 seconds.