The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+277x^34+272x^35+731x^36+812x^37+1567x^38+984x^39+1666x^40+712x^41+575x^42+240x^43+203x^44+44x^45+73x^46+8x^47+20x^48+4x^50+2x^52+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 58.3 seconds.