The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  0  2  0  1  1  2  1  1 12  0  4  2  1  0  1  1 12  4  1  1  1
 0  2  0  2  0  2 12 14  4 14 12  6 12  2 10  8 10  8  6  2  2  4  6  8  8  4  2  2  0  0  4  4 10  2  8 10  0  8
 0  0  2  2 12  6  6 12  4  6  2  4 12  6  6  6  4  2  4  0 10  0  8  6 10  2 14  0  2  6  2  8  8 12  2 10 12  0
 0  0  0  4  0  4  0  0  8 12  4  4 12  8  0  4  4  0  4  8  8  4  0 12  4  4 12  4  4 12 12  4  0 12 12  0 12 12
 0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  0  8  0  0  8  8  8  0  8  8  8  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  8  8  8  0  8  8  8  8  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8
 0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+58x^30+112x^31+506x^32+616x^33+1242x^34+2172x^35+4039x^36+4644x^37+5713x^38+5068x^39+4032x^40+2052x^41+1341x^42+564x^43+363x^44+108x^45+89x^46+20x^47+16x^48+4x^49+5x^50+2x^52+1x^56

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 9.28 seconds.