The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^30+84x^31+238x^32+482x^33+671x^34+1816x^35+4920x^36+6074x^37+13570x^38+9710x^39+13726x^40+6070x^41+4740x^42+1870x^43+764x^44+414x^45+151x^46+86x^47+59x^48+16x^49+27x^50+2x^51+4x^52+2x^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 25 seconds.