The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  0  2  1  4  1  2  0  1  1  4  2  1  1
 0  2  0  2  0 10 12 14  4  4  6  6 10  2  0  4 14  2  4 14  2 12  4  2  6  4  0
 0  0  2  2 12 14  6  4  2  4  6  0  6  0  2  2  2  4 10  4  6  4  2  2  8 10  0
 0  0  0  8  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0  0  0  8  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  8  0  8  0  0  8  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  0  8  0  0  0  8  8  8  8  8  0  8  0  8  8
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  8  0  8  8  8  0  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+17x^20+70x^21+252x^22+386x^23+1189x^24+1606x^25+2891x^26+3582x^27+2903x^28+1590x^29+1191x^30+366x^31+230x^32+58x^33+17x^34+18x^35+12x^36+4x^37+1x^38

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 1.36 seconds.