The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^32+110x^33+252x^34+360x^35+540x^36+930x^37+1272x^38+1336x^39+1108x^40+942x^41+656x^42+264x^43+144x^44+118x^45+56x^46+24x^47+20x^48+12x^49+4x^50+4x^52

The gray image is a code over GF(2) with n=312, k=13 and d=128.
This code was found by Heurico 1.16 in 0.729 seconds.