The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1  1 12 10  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  0  3  1  6  5  1 12 15  5  1  1  9  6  9  3 15  9  3  3 11  9  1 15 11  3  6  6
 0  0  8  0  0  0  0  8  0  8  8  8  0  0  0  8  8  8  0  0  0  8  8  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0
 0  0  0  8  0  0  8  8  0  8  0  8  0  8  8  8  0  0  8  0  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0
 0  0  0  0  8  0  8  0  8  8  8  8  0  8  0  0  8  0  0  8  8  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  8  0  0  0  8  0  8  0  8  8  8  0  0  0  0  0  8  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+35x^34+200x^35+135x^36+736x^37+349x^38+1200x^39+345x^40+736x^41+118x^42+200x^43+29x^44+6x^46+2x^48+2x^50+1x^58+1x^62

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 0.183 seconds.