The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^21+314x^22+510x^23+1160x^24+1690x^25+2806x^26+3104x^27+3068x^28+1752x^29+1030x^30+430x^31+279x^32+90x^33+42x^34+20x^35+4x^36

The gray image is a code over GF(2) with n=216, k=14 and d=84.
This code was found by Heurico 1.16 in 1.61 seconds.