The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  8  8  1  2  1  1  2  1  0  2  1  2 12  1  2  2  2
 0  2  0  6  0  6  2  4  4  6 10 12  0  6  4 10 14 12  6  2 14  2  2  2  6  8 10 10  6  2  4 14  2  2 14  4  6 14
 0  0 12  0  0  0  0 12  8  4 12  0  4  8  4 12  0  4  8  4  4  0  0 12  4  8  8 12 12 12  0  8  0 12 12  8  0  4
 0  0  0 12  0  0  4  8  0  0  8  0  4 12 12  4  8  0  0  8  4 12  8 12  0 12 12 12  0 12  0  8  4  8 12  0 12  8
 0  0  0  0 12  0  0  0  4  4 12  8  8  4  4  8  4 12  0  0 12  0  4  4 12  8  4  0  8  8 12  4  8 12  0 12  4  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  0  0  0  8  8  8  8  0  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  8  8  8  8  0  0  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+174x^30+68x^31+603x^32+408x^33+1419x^34+1596x^35+4013x^36+5072x^37+5984x^38+5116x^39+4164x^40+1624x^41+1327x^42+388x^43+506x^44+64x^45+178x^46+56x^48+5x^50+1x^52+1x^58

The gray image is a code over GF(2) with n=304, k=15 and d=120.
This code was found by Heurico 1.16 in 10.7 seconds.