The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  1  1  0  1  0  1  2  1  2  1  1  2  1  1  1  1  1  1  8  1  8  8  8  1
 0  2  0  6  0 14  0  6  2 12  6  4 14  2  6  6  8  2 14  2  2 14 12  6 10  4 10 14  0  6  2  0  6  2  4  2  2  2  0
 0  0 12  0  0  0  4  4  4  8  0  4  0  4  8  4  8  8  8  4 12  4 12  4  0 12  0  0  8  8  4 12  0  4  8  8  4 12  0
 0  0  0 12  0  0  0  0  0  0  0  0  8  8  8 12  4 12  4  4  4  8  4  4 12  8  4  8 12  8 12  0  4  0 12  8 12  8  0
 0  0  0  0 12  4  4  4  8  0  0  0 12 12  8  0  0 12 12  8  4  0 12  8  4  8  4 12  0  8  0  8  0  0  4  4 12  0  0
 0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  8  0  0  8  0  0  8  0  8  0  0  8  0  8  0  8  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  8  0  8  8  0  0  0  8  0  0  8  0  0  8  8  0  8  0  8  0  8  0  8  8  8  8  8  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+52x^30+98x^31+216x^32+342x^33+576x^34+1224x^35+2109x^36+3646x^37+5244x^38+5770x^39+5241x^40+3668x^41+2141x^42+1202x^43+549x^44+328x^45+161x^46+84x^47+66x^48+14x^49+15x^50+6x^51+10x^52+2x^53+3x^54

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 10.8 seconds.