The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  1  1 12  2  1  1 10  1  0  1  1  1  8  2  8
 0  1 11 14  5  1  0  3  1  6  1  9 13  4  1  1  7 10  1  2  1 15  8 14  1  8  1
 0  0 12  4  0  4 12  0  8  8 12  0  4  4  0  4  4  8  8  4  0  0 12 12 12  4  4
 0  0  0  8  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  8  8  0  0  8  0  8
 0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  8
 0  0  0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  0  8  0  0  0  8  8  8  0  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+50x^20+102x^21+216x^22+638x^23+873x^24+5830x^25+3456x^26+10446x^27+3489x^28+5762x^29+896x^30+682x^31+181x^32+82x^33+32x^34+10x^35+12x^36+8x^38+1x^40+1x^44

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 3.75 seconds.