The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+208x^31+247x^32+656x^33+770x^34+1464x^35+1620x^36+1514x^37+688x^38+506x^39+200x^40+196x^41+45x^42+60x^43+12x^44+2x^45+2x^47+1x^58

The gray image is a code over GF(2) with n=288, k=13 and d=124.
This code was found by Heurico 1.16 in 0.625 seconds.