The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  0  2  2 12  1  1  2  4  1  2  1  1  1  1  2  2  2  1  2
 0  2  0  6  0 14 10  8  6  8  2  8  0  8  6  2  6  2  2  6  2  2  4 14  2  2 12  6  2 12  4  6 14  6  6  6  6
 0  0 12  0  0  0  0  4  4  8  4  4  8 12  4  4  0  8  8  4 12  4  4  4  8 12  0  4  8 12  4  0  8  4  4  8  8
 0  0  0 12  0  8 12  0 12  4 12 12  4 12  0  8  0  0  4 12  8  8  0  8 12 12 12  8  0  4 12  8  0  4  0 12  4
 0  0  0  0 12 12  4 12  8  0 12  4 12  8 12  0  8 12 12  0  0 12  0  8  0  4 12 12  4  8 12  8  4  4 12  4  4

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

Homogenous weight enumerator: w(x)=1x^0+60x^31+236x^32+348x^33+512x^34+1110x^35+812x^36+2126x^37+752x^38+1080x^39+574x^40+322x^41+132x^42+48x^43+36x^44+18x^45+8x^46+4x^47+5x^48+2x^49+4x^50+2x^51

The gray image is a code over GF(2) with n=296, k=13 and d=124.
This code was found by Heurico 1.16 in 6.61 seconds.