The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^31+435x^32+1036x^33+2627x^34+3564x^35+6027x^36+5300x^37+6107x^38+3614x^39+2511x^40+884x^41+409x^42+114x^43+49x^44+12x^45+9x^46+6x^47+1x^48+2x^51

The gray image is a code over GF(2) with n=296, k=15 and d=124.
This code was found by Heurico 1.16 in 4.97 seconds.