The generator matrix

 1  0  1  1  1 14  1  1  0  1  1 14  1  1  0  1  6  1  1  1  2  1  1  1  1 10  1  1  1 10  1  1  1  8  1  8 14  1  1
 0  1 11  6  1  1  0  3  1  6  5  1 10  5  1 11  1  0 14 13  1 10 15  3 14  1 13  5  7  1  6  9  8  1  0  2  1  8  0
 0  0 12  0  0  0  0  4  4 12  0  4  8  4  0  4  4  4  4 12 12  4  4  8  8  0  8  4  4 12 12  4  4  8  0  0 12  4  0
 0  0  0 12  0  0  0  0  0  0  8  8  4  4 12  4 12 12  4  4  8  0 12 12  8  4  4  0  0  4  4  4  8  8  8 12 12  8  0
 0  0  0  0  4  4 12  4  4  4  8  0 12  8  4 12  8  8 12  4  0 12  0 12  4  4  8  4  8  0  0  0  8 12  8  0 12  8  0
 0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0
 0  0  0  0  0  0  8  8  8  0  8  0  8  0  0  8  8  0  8  0  8  8  8  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  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+92x^31+223x^32+428x^33+843x^34+2014x^35+4058x^36+7734x^37+11267x^38+12260x^39+10998x^40+7692x^41+4296x^42+2064x^43+739x^44+376x^45+146x^46+80x^47+106x^48+24x^49+21x^50+2x^51+2x^52+2x^53+1x^54+1x^60

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 25.5 seconds.