The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  0  2  0  2  2  8  2  1  1  1  4  2  2  1  2  1
 0  2  0  2  0  0  2 10  8  0  6  6  4  2 14 12  6 12 10  6 12  2  6  2  4 12  4 12  2 10 10  8 12 12  6 10  2  8  8
 0  0  2  2  0  6 10  8  6  4  6 12 12 12 10  2  8 12  6  4  6 14  4  4 10  2 14 14  4  8  4 10 12  0  2  2  2  4 14
 0  0  0  4  0  0  4  0  0  0 12  0  0  0  4  8  8  0 12  8  8  8 12  0 12  8  0 12  8 12  4 12 12  4  4  0  8  4  4
 0  0  0  0 12  0 12  4  4  4 12  4  8  0  8 12  4  4  4  8  0 12  8 12  8  4  0  8  8 12  4  4  0  8  4  8  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  8  8  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+312x^32+268x^33+876x^34+1288x^35+2474x^36+3424x^37+4950x^38+5340x^39+5290x^40+3596x^41+2372x^42+1152x^43+808x^44+264x^45+232x^46+28x^47+69x^48+16x^50+6x^52+2x^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 37.9 seconds.