The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  1  1  2  1  1  1  1  4  2  2  0  1  1  1  1  2  4  1  1
 0  2  0  6  4 14 12  2  0  6 12 10  8  2 12  6 14  2  0  6 12 10  2  6 12  0 12  2  6 10  2 10 14  4  6  4  2  6  6
 0  0 12  0  4  4  8  4  0  8  0  8  4  4 12  4  4  4  8  0  8  0  4  0  8  4 12 12  8  0  0  0 12 12  4 12 12  0  4
 0  0  0  8  0  0  8  0  0  8  0  0  8  0  8  0  8  8  8  8  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8  8  8  0  0
 0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  8  8  0  0  0  8  0  8  8  8  0  8  0  0  8  0  0  0  0  8  0  8  8  8
 0  0  0  0  0  8  0  8  0  0  8  8  8  0  8  0  8  8  8  8  8  8  0  8  8  8  0  0  8  8  0  0  0  0  0  8  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+156x^34+124x^35+192x^36+636x^37+440x^38+1048x^39+396x^40+632x^41+242x^42+108x^43+47x^44+12x^45+54x^46+3x^48+2x^50+2x^54+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 87.5 seconds.