The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+160x^30+24x^31+555x^32+328x^33+1278x^34+1688x^35+3940x^36+5128x^37+6572x^38+5128x^39+3971x^40+1688x^41+1310x^42+328x^43+442x^44+24x^45+138x^46+48x^48+12x^50+2x^52+2x^54+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 11.2 seconds.