The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+184x^31+524x^32+1206x^33+1944x^34+3958x^35+5064x^36+7016x^37+5126x^38+4006x^39+2013x^40+1026x^41+332x^42+228x^43+91x^44+28x^45+6x^46+6x^47+2x^48+4x^49+2x^51+1x^52

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 6.2 seconds.