The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+230x^34+364x^35+712x^36+816x^37+1464x^38+1264x^39+1309x^40+816x^41+586x^42+252x^43+236x^44+64x^45+52x^46+8x^47+13x^48+4x^50+1x^56

The gray image is a code over GF(2) with n=312, k=13 and d=136.
This code was found by Heurico 1.16 in 0.671 seconds.