The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+56x^31+99x^32+274x^33+137x^34+768x^35+664x^36+2268x^37+2144x^38+3472x^39+2314x^40+2336x^41+503x^42+768x^43+212x^44+228x^45+16x^46+56x^47+32x^48+14x^49+15x^50+4x^52+2x^56+1x^58

The gray image is a code over GF(2) with n=312, k=14 and d=124.
This code was found by Heurico 1.16 in 4.48 seconds.