The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+122x^31+513x^32+1092x^33+2339x^34+4430x^35+7514x^36+10934x^37+11491x^38+11148x^39+7602x^40+4432x^41+2333x^42+920x^43+390x^44+176x^45+57x^46+18x^47+12x^48+4x^49+4x^50+2x^51+2x^53

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 24.1 seconds.