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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+80x^32+484x^33+955x^34+1404x^35+2330x^36+3628x^37+4779x^38+5340x^39+5036x^40+3674x^41+2224x^42+1412x^43+766x^44+394x^45+164x^46+36x^47+43x^48+10x^49+5x^50+2x^53+1x^54

The gray image is a code over GF(2) with n=312, k=15 and d=128.
This code was found by Heurico 1.16 in 9.22 seconds.