The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+190x^31+945x^32+2760x^33+4523x^34+8052x^35+9718x^36+12938x^37+10186x^38+8244x^39+4212x^40+2426x^41+927x^42+296x^43+70x^44+34x^45+4x^46+2x^47+6x^48+2x^49

The gray image is a code over GF(2) with n=296, k=16 and d=124.
This code was found by Heurico 1.16 in 16.9 seconds.