The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  1 12  1  1  2  0  1  2 12  1  1  1  2  1  1  0  2  1  2  1  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2  0 10  6  2 12 10  6  2  0 10  2 12 10  0  6  6  0  2  6  0 12 10  6  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  8  0  8  0  0  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  0  0  0  0  8  8  8  0  0  8  8  0  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  0  8  8  8  0  0  0  0  8  0  8  0  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  8  0  8  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  8  0  0  8  0  0  0  0  8  8  0  0  8  8  8  8  8  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  0  8  8  8  0  8  8  0  8  0  8  8  0  0  8  0  0  8  8  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+6x^29+58x^30+108x^31+157x^32+294x^33+318x^34+1300x^35+1910x^36+2328x^37+3316x^38+2540x^39+1944x^40+1160x^41+316x^42+380x^43+52x^44+50x^45+82x^46+24x^47+26x^48+2x^49+6x^50+6x^52

The gray image is a code over GF(2) with n=304, k=14 and d=116.
This code was found by Heurico 1.16 in 69.6 seconds.