The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+32x^31+271x^32+248x^33+806x^34+1252x^35+2162x^36+3796x^37+4942x^38+5684x^39+5066x^40+3892x^41+2106x^42+1196x^43+730x^44+252x^45+202x^46+28x^47+78x^48+4x^49+8x^50+12x^52

The gray image is a code over GF(2) with n=312, k=15 and d=124.
This code was found by Heurico 1.16 in 12.6 seconds.