The generator matrix

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

generates a code of length 29 over Z16 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+16x^21+75x^22+300x^23+398x^24+1540x^25+3181x^26+8444x^27+9630x^28+18292x^29+9692x^30+8452x^31+3229x^32+1612x^33+344x^34+212x^35+42x^36+44x^37+17x^38+12x^40+3x^42

The gray image is a code over GF(2) with n=232, k=16 and d=84.
This code was found by Heurico 1.16 in 14 seconds.