The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^34+272x^35+129x^36+504x^37+196x^38+524x^39+122x^40+200x^41+28x^42+32x^43+2x^44+4x^47+1x^48+1x^50+1x^68

The gray image is a code over GF(2) with n=304, k=11 and d=136.
This code was found by Heurico 1.16 in 0.0468 seconds.