The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  1  1 12  1  1  1  1 10  0  1  1  6  1  0  1  0  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  5  1  6  3  1 12 10 15  9  1  0  3  6  5  1  1 15 10  1  3  1  0  1  0  0
 0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0  8  0  8  0  8  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  8  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  0  8  8  0  0  0  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  0  8  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  0  0  0  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  8  8  0  8  0  8  0  0  0  8  0  0  8  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+54x^28+60x^30+16x^31+435x^32+240x^33+976x^34+2256x^35+3747x^36+5680x^37+5864x^38+5680x^39+3730x^40+2256x^41+976x^42+240x^43+412x^44+16x^45+60x^46+57x^48+11x^52+1x^64

The gray image is a code over GF(2) with n=304, k=15 and d=112.
This code was found by Heurico 1.16 in 5.73 seconds.