The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^21+222x^22+442x^23+933x^24+1868x^25+3348x^26+7318x^27+11758x^28+13394x^29+11964x^30+7334x^31+3535x^32+1858x^33+820x^34+378x^35+154x^36+92x^37+30x^38+16x^39+3x^40+2x^41

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 23.4 seconds.