The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+20x^30+68x^31+271x^32+462x^33+1060x^34+2286x^35+3965x^36+8374x^37+10010x^38+12550x^39+10065x^40+8146x^41+4061x^42+2426x^43+1002x^44+418x^45+200x^46+78x^47+46x^48+8x^49+6x^50+9x^52+2x^54+1x^56+1x^58

The gray image is a code over GF(2) with n=312, k=16 and d=120.
This code was found by Heurico 1.16 in 23 seconds.