The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  8  1  8  2  1  1  2  1  2  1  1  1
 0  2  0  6  0  6  0  2  4 10  8 14  2 14  6  2  0  2 14 12  6 10 14 14  6 14  8
 0  0 12  0  0  4  4  4 12  4  8  0  8 12 12  0  8  4 12  4  0  8  4  0  0  0  0
 0  0  0 12 12  4  4  0  8 12 12  4  8  0  4  4  0  8  0  4 12  0  0 12  8  0  4
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0
 0  0  0  0  0  0  8  8  8  8  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+52x^20+86x^21+195x^22+430x^23+782x^24+1826x^25+3086x^26+3502x^27+3050x^28+1854x^29+769x^30+410x^31+201x^32+70x^33+42x^34+10x^35+10x^36+4x^37+3x^38+1x^46

The gray image is a code over GF(2) with n=216, k=14 and d=80.
This code was found by Heurico 1.16 in 1.6 seconds.