The generator matrix

 1  0  0  1  1  1  2 10  1  1 12  1  1  4 14  2  1  1  1  6  1  1 10  1  4  1  1  1  1  1  1  1  1 12  1  4  1  1
 0  1  0  0 13 13  1  6  8  5  1 14 11  1  1  4  7  6  4  1  2  3  1 15 14  9  2 10  4  0 15 12 15  0  6  1  6 12
 0  0  1  3  7  4  7  1 14  5  5  9  2  2  9  1  8  6  1  2 11  9  0  7  1  6 13 12  0  9 15  2  4  1  3  4  8  6
 0  0  0  8  8  0  8  8  0  0  0  0  8  8  0  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  0  0  8  0

generates a code of length 38 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+219x^34+800x^35+1177x^36+1260x^37+1598x^38+1180x^39+887x^40+608x^41+292x^42+96x^43+43x^44+20x^45+2x^46+4x^47+4x^48+1x^50

The gray image is a code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 0.375 seconds.