The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  1  1  1 12  1  2  1 10  1  1  1  8  1  2  1  1  1
 0  1 11 14  5  1  0  3  1  6  1 13 12 15 10  1  9  1  7  1  1  6  0  1  3  8 11 11  0
 0  0 12  4  0  4 12  0  0  8 12  4  0  8  0  0  8  4  4  0  4  8  0 12  0  4  4  4  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  0  8  8  0  0  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  8  8  8  0  8  8  0  8  8  0  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  0  8  8  8  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  8  0  0  0  8  8  8  8  8  0  8
 0  0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  0  8  8  8  0  0  0  0  0  8  0

generates a code of length 29 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+42x^20+40x^21+93x^22+162x^23+606x^24+832x^25+3688x^26+8024x^27+11948x^28+14640x^29+11962x^30+8044x^31+3693x^32+832x^33+608x^34+152x^35+82x^36+40x^37+33x^38+2x^39+11x^40+1x^56

The gray image is a code over GF(2) with n=232, k=16 and d=80.
This code was found by Heurico 1.16 in 13.4 seconds.