The generator matrix

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

generates a code of length 27 over Z16 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+68x^21+296x^22+548x^23+1872x^24+3588x^25+6290x^26+7488x^27+6310x^28+3568x^29+1820x^30+532x^31+259x^32+68x^33+42x^34+8x^35+6x^36+4x^37

The gray image is a code over GF(2) with n=216, k=15 and d=84.
This code was found by Heurico 1.16 in 5.3 seconds.