The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  0  1  1  2  1  2  1 12  2  1  8  1  1  1  2 12  1  1  4  2
 0  2  0  6  4  6 12  2  8  0  6 14  4  4  2 10  6  2 14  2  8 14  6 12 10  6  2  2  6  2 12  4 14  6  2  4  0  2  0
 0  0 12  0  4  0  0  8  0  4  4 12  8  4 12 12  8  0  8  8  0 12  4  0 12  4  8  8  0  4  4  4  0 12  4  4  4  4  0
 0  0  0 12  0  0  8  4  4  4  4  8 12  4  0  4  0 12  4  8 12  0 12  8 12  4  0 12  8  0  4 12  8  0  4  8  4  0  4
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  8  8  8  8  8  0  0  0  0  8  0  0  8  8  0  8  0  8  8  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+119x^34+148x^35+334x^36+548x^37+617x^38+664x^39+566x^40+536x^41+283x^42+148x^43+76x^44+4x^45+27x^46+9x^48+10x^50+6x^52

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 0.233 seconds.