The generator matrix

 1  0  1  1  1  4  1  1 10  1  6  1  1  1 10  2  1  1  1 12  1  1  8  1  8 14  0  1  0  2  1  4  1  1  2  4  1 12  1
 0  1  1  0 11  1  2  7  1  5  1 14  9  2  1  1  3  6 12  1  8 13  1 15  2  1  1  5  1  8  0  8  7 10 10  1  5  1 14
 0  0  2  6  0  2  2 14 10  8  4  0  6 14 14 12 12 12 14 10  4  4  4  6  2  8 10  2 10  2 14  2  8  6 14  0  4 14  4
 0  0  0 12  0  0  8  4 12 12  4  4  8 12  0  8  0  8  8 12  8 12  4  4  8  8  8  4  0 12 12  0  4  0  0  0 12  4  4
 0  0  0  0 12  0  0  0  0  4  0  0  0  0  0  0  4 12  8  8  8  4 12 12  8  4 12  8  4 12 12  8  8 12  4  8  0  4  4
 0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  0  8  0  0  8  8  0  8  0  0  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+245x^32+384x^33+1208x^34+2396x^35+4297x^36+7612x^37+10464x^38+12060x^39+10878x^40+7532x^41+4472x^42+2388x^43+896x^44+340x^45+224x^46+52x^47+60x^48+4x^49+16x^50+7x^52

The gray image is a code over GF(2) with n=312, k=16 and d=128.
This code was found by Heurico 1.16 in 38.6 seconds.