The generator matrix

 1  0  0  1  1  1 10  4  2  0  1  1  1  1  1  2  4  1 14  1  8  1  1  1  6 10  1  1  6 10 14  2  1  1 14  1  1
 0  1  0  4  5  1  1  1  1  6 10  0 15 11  2  1  1  3  2  5  1 15  1 10  1  0 12  7  1 12  1  8  8  9  1 14  0
 0  0  1  7  3  4  3  2  1  1  5  6  3  2  2  4  7  5  1  6  1  0  1  0  0  1  8  4 14  1 14  1 10  2 15  4  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  8  8  8  0  0  8  8  0  8  0  8  0  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  0  0  8  8  0  8  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+72x^31+453x^32+1268x^33+2173x^34+3934x^35+4944x^36+6734x^37+5350x^38+4272x^39+1976x^40+1002x^41+400x^42+104x^43+48x^44+18x^45+10x^46+2x^48+2x^49+3x^50+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 4.83 seconds.