The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  4  4  4  1  1  2  2  4  1  4  2  4  2
 0 12  0  0  0  4 12  4  0  8  0 12  0  0  4 12 12  4  8  8  0  8  0  8 12  4  4  0 12 12  0 12  4  4  8  0  8  0  4
 0  0 12  0  4  4 12  0  0  0 12  8  0 12  4  8  4  0  8  4 12  8  4  0  0  8  4  8  0 12  4  4 12  8  8 12  8  8  4
 0  0  0 12  4  0 12  4  0  4 12 12  8  8  0  8 12 12 12  4  0  8  4  4  8  4  0  4  8 12  8 12  0 12  4  8 12  4  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  0  0  8  8  0  8  0  8  8  8  8  0  0  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  0  0  0  8  0  8  0  0  0  8  8  8  0  0  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  8  8  8  8  0  0  8  8  0  8  0  8  0  0  0  8  0  0  0  8  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  8  8  8  0  8  0  0  0  8  8  0  0  8  0  8  8  8

generates a code of length 39 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+32x^29+127x^30+186x^31+329x^32+508x^33+475x^34+1586x^35+1614x^36+4054x^37+3595x^38+7704x^39+3587x^40+4100x^41+1667x^42+1624x^43+500x^44+488x^45+245x^46+158x^47+97x^48+32x^49+33x^50+6x^51+14x^52+2x^53+1x^54+1x^56+1x^58+1x^64

The gray image is a code over GF(2) with n=312, k=15 and d=116.
This code was found by Heurico 1.16 in 14.2 seconds.