The generator matrix

 1  0  1  1  1  4  1  1  6  1  2  1  1  1  8  0  2  1  1  1  1  1  1 10 14  1  1 14  1  2  1  1  0  1 14  8  6  4  0
 0  1  1  4  3  1  2  7  1 14  1  9 13  8  1  1  1  3 10  4 10  1 11  1  1 14  5  1 14  4 15  0  1  7  1  4  1  2  1
 0  0  2  2  0  2  2 10  0  4  2 14  4  2 12  6 10  6  6  4  8 12  4  0  2 12  0 12 12  2 14  8  0 10 14  2 14  2  0
 0  0  0  8  0  0  0  8  8  0  0  8  8  8  8  8  8  8  8  8  0  0  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  0  8  0  8  8  8  0  8  0  8  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  8  8  8  0  8  8  8  8  8  0  0
 0  0  0  0  0  0  8  8  8  0  0  8  8  0  0  0  0  0  8  0  0  8  8  0  8  8  0  0  8  8  8  0  8  8  8  8  8  0  8

generates a code of length 39 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+46x^32+260x^33+432x^34+1372x^35+1725x^36+4844x^37+3963x^38+7562x^39+3976x^40+4866x^41+1670x^42+1274x^43+376x^44+266x^45+68x^46+30x^47+17x^48+2x^49+10x^50+2x^51+3x^52+2x^53+1x^54

The gray image is a code over GF(2) with n=312, k=15 and d=128.
This code was found by Heurico 1.16 in 6.56 seconds.