The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+207x^30+64x^31+624x^32+984x^33+2193x^34+4156x^35+8201x^36+9992x^37+12431x^38+10476x^39+8039x^40+4040x^41+2389x^42+916x^43+507x^44+88x^45+173x^46+4x^47+36x^48+14x^50+1x^62

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 26 seconds.