The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^34+60x^35+219x^36+44x^37+423x^38+392x^39+567x^40+72x^41+110x^42+60x^43+45x^44+12x^45+4x^46+1x^70

The gray image is a code over GF(2) with n=312, k=11 and d=136.
This code was found by Heurico 1.16 in 0.0914 seconds.