The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^34+230x^35+292x^36+492x^37+589x^38+918x^39+557x^40+454x^41+208x^42+150x^43+73x^44+44x^45+17x^46+14x^47+4x^48+2x^49+2x^50+1x^60

The gray image is a code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.194 seconds.