The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+42x^29+113x^30+178x^31+321x^32+538x^33+1120x^34+2206x^35+3766x^36+5212x^37+5750x^38+5240x^39+3796x^40+2236x^41+1114x^42+528x^43+270x^44+154x^45+87x^46+38x^47+32x^48+10x^49+6x^50+2x^51+4x^52+2x^54+2x^56

The gray image is a code over GF(2) with n=304, k=15 and d=116.
This code was found by Heurico 1.16 in 10.2 seconds.