The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  1  0  1  1  1  2  4  1  1  2  1 12  1  1  0  2  1  1  2  8  2  1
 0  2  0  6  4 14 12  2  0  6  8 10 12  6  2 14 14  2  4 14  4  2  2  0  6 10  0  2  6  2  2 12 14 10  6  2  4  0
 0  0 12  0  4  4  0  4  0  8 12  8  0  0  4  4 12  8 12  4  4 12 12  0  8  0  0  8  0 12  8 12 12  8  0  4 12  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  8  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  8  0  0  8  8  8
 0  0  0  0  0  8  0  0  8  8  8  0  0  8  8  8  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  0  0  0  8  0  0  8  8  8  8  8  0  8  8  8  0  8  8  0  8  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  0  8  0  8  8  0  8  0  8  8  8  0  0  0  0  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+63x^30+84x^31+199x^32+242x^33+550x^34+1188x^35+1618x^36+2600x^37+3383x^38+2572x^39+1560x^40+1180x^41+560x^42+236x^43+184x^44+72x^45+41x^46+16x^47+16x^48+2x^49+10x^50+6x^52+1x^54

The gray image is a code over GF(2) with n=304, k=14 and d=120.
This code was found by Heurico 1.16 in 2.76 seconds.