The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+66x^31+380x^32+912x^33+2274x^34+4652x^35+7128x^36+11712x^37+11124x^38+11876x^39+7254x^40+4708x^41+2180x^42+796x^43+324x^44+72x^45+36x^46+18x^47+13x^48+4x^49+2x^50+4x^52

The gray image is a code over GF(2) with n=304, k=16 and d=124.
This code was found by Heurico 1.16 in 18.7 seconds.