The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^31+424x^32+788x^33+1725x^34+2728x^35+4607x^36+7182x^37+9519x^38+11162x^39+9717x^40+7480x^41+4881x^42+2546x^43+1421x^44+664x^45+381x^46+140x^47+86x^48+12x^49+6x^50+6x^51+2x^53

The gray image is a code over GF(2) with n=312, k=16 and d=124.
This code was found by Heurico 1.16 in 34.5 seconds.