The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^34+100x^35+298x^36+304x^37+477x^38+280x^39+253x^40+48x^41+88x^42+36x^43+19x^44+13x^46+4x^48+1x^60

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 0.102 seconds.