The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+29x^28+54x^29+98x^30+272x^31+286x^32+1108x^33+1307x^34+4746x^35+7880x^36+10180x^37+13585x^38+10224x^39+7879x^40+4784x^41+1299x^42+1092x^43+269x^44+246x^45+84x^46+48x^47+33x^48+12x^49+9x^50+2x^51+6x^52+1x^54+1x^56+1x^58

The gray image is a code over GF(2) with n=304, k=16 and d=112.
This code was found by Heurico 1.16 in 22.1 seconds.