The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+148x^32+454x^33+1112x^34+2234x^35+4279x^36+7466x^37+10762x^38+12406x^39+10960x^40+7666x^41+4384x^42+2070x^43+912x^44+406x^45+180x^46+58x^47+19x^48+8x^49+8x^50+1x^52+2x^54

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 24.6 seconds.