The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+196x^28+64x^29+618x^30+804x^31+2501x^32+4236x^33+8044x^34+10284x^35+12022x^36+10260x^37+8132x^38+4188x^39+2608x^40+788x^41+492x^42+84x^43+142x^44+12x^45+58x^46+1x^48+1x^64

The gray image is a code over GF(2) with n=288, k=16 and d=112.
This code was found by Heurico 1.16 in 23.5 seconds.