The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^30+166x^31+484x^32+1056x^33+2282x^34+4638x^35+7350x^36+10906x^37+11350x^38+11274x^39+7537x^40+4634x^41+2090x^42+922x^43+482x^44+158x^45+86x^46+24x^47+17x^48+14x^49+4x^50+1x^56

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 23.6 seconds.