The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  0  1  1  1  1  6  1  8  1  0  1  1  1  1  1
 0  1 11  6  1  1  0  3  1 14  1  5  1 14 11  8 11  1 12  1 15  4  8 12  3 11  0
 0  0 12  0  0  0  0  0  0  8  8  4  4 12  8 12 12  4  8 12 12  8  4  0  8  8  0
 0  0  0 12  0  0 12  8 12  8  4  4 12  0 12 12  4  8  8  0  8  4  0  4 12  8  0
 0  0  0  0  4  4 12  8  4 12  0  8  8  0  8  4  4  4  0  0  4  0  0  4  4  4  0
 0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  0  0  8  0  8

generates a code of length 27 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+52x^20+126x^21+268x^22+734x^23+1571x^24+3624x^25+6386x^26+7314x^27+6166x^28+3832x^29+1614x^30+642x^31+259x^32+96x^33+46x^34+14x^35+14x^36+2x^37+6x^38+1x^40

The gray image is a code over GF(2) with n=216, k=15 and d=80.
This code was found by Heurico 1.16 in 3.99 seconds.