The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+196x^31+840x^32+2632x^33+4153x^34+7696x^35+10941x^36+12414x^37+11211x^38+8038x^39+4051x^40+2212x^41+703x^42+316x^43+79x^44+22x^45+13x^46+10x^47+8x^48

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 19.2 seconds.