The generator matrix

 1  0  1  1  1 14  1  1 14  1  0  1  1  6  1  1  1  1  2  1 14  1  1  1  1  8  1
 0  1 11  6  5  1 11  0  1 14  1 13  6  1  8  3  5 15  1  7  1  2  4  1  7  1  8
 0  0 12  0  0  0  0  4  4  4  4  4  4  8  0  8 12  4  8  8  8  8 12  4  8 12  4
 0  0  0 12  0  4  4  4  8  8 12  8  4  8 12  0 12 12  4 12  4  4  0  0 12  8  0
 0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  8  8  0  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  0  8  8  0  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+60x^20+82x^21+216x^22+420x^23+1749x^24+3384x^25+7192x^26+6564x^27+7192x^28+3388x^29+1756x^30+428x^31+201x^32+56x^33+48x^34+12x^35+12x^36+2x^37+4x^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 3.8 seconds.