The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^30+114x^31+236x^32+470x^33+884x^34+1926x^35+3935x^36+7442x^37+11197x^38+12870x^39+11401x^40+7406x^41+3883x^42+2014x^43+873x^44+406x^45+205x^46+96x^47+62x^48+20x^49+19x^50+4x^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 26.3 seconds.