The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^21+506x^22+1604x^23+3540x^24+7516x^25+12041x^26+14662x^27+12600x^28+7674x^29+3298x^30+1392x^31+483x^32+120x^33+42x^34+6x^35+4x^37+1x^42

The gray image is a code over GF(2) with n=216, k=16 and d=84.
This code was found by Heurico 1.16 in 11.9 seconds.