The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+848x^31+2435x^32+4784x^33+7553x^34+11474x^35+11409x^36+11314x^37+8036x^38+4764x^39+1790x^40+796x^41+233x^42+66x^43+29x^44+2x^45+2x^46

The gray image is a code over GF(2) with n=288, k=16 and d=124.
This code was found by Heurico 1.16 in 88.1 seconds.