The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^30+114x^31+198x^32+432x^33+542x^34+1620x^35+2022x^36+4114x^37+4355x^38+5782x^39+4384x^40+4282x^41+2032x^42+1586x^43+504x^44+374x^45+171x^46+112x^47+47x^48+14x^49+18x^50+2x^51+10x^52+1x^54+2x^56

The gray image is a code over GF(2) with n=312, k=15 and d=120.
This code was found by Heurico 1.16 in 10.6 seconds.