The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+850x^31+2398x^32+5094x^33+7140x^34+11410x^35+11497x^36+11750x^37+7610x^38+4790x^39+1897x^40+818x^41+160x^42+102x^43+15x^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 20.5 seconds.