The generator matrix

 1  0  1  1  1  4  1 10  1  6  1  1  1 10  1  1  1  1  0  1 12  4  1  1 12  1  2  4  1  1 12  1  1  1  1  1  4  1
 0  1  1  0 11  1  6  1 13  1  7  2 14  1 13  0  7 12  4  5  1  1 15  1  1  8  0  2  2  4  2  6  2  9  0  3  1  0
 0  0  2  6  0  2  0  2  4  4  6  2  8  6  8  2 14  4  2  4  8 14  2 14  8 12  6  2 12  4  6 14 14 12  8  6  6  0
 0  0  0 12  0  4  4  8 12  4 12 12  8  8  4  8  0  4  8  0  0  4  4  0  4  4 12 12  8  4 12  0  4  0  4  8  4  0
 0  0  0  0 12  4  4 12  4  8  0 12 12  0  8 12  4  0 12  0 12  8  0 12 12 12  4  4  8  0  4  0  0  8  4  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  0  0  0  8  0  0  8  0  8

generates a code of length 38 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+57x^30+180x^31+449x^32+978x^33+2195x^34+4498x^35+7697x^36+10178x^37+12966x^38+10382x^39+7820x^40+4354x^41+2106x^42+974x^43+390x^44+158x^45+81x^46+30x^47+26x^48+12x^49+3x^50+1x^52

The gray image is a code over GF(2) with n=304, k=16 and d=120.
This code was found by Heurico 1.16 in 23.8 seconds.