The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^32+222x^33+523x^34+1504x^35+1975x^36+4082x^37+4663x^38+6738x^39+4626x^40+4370x^41+1820x^42+1228x^43+543x^44+230x^45+85x^46+50x^47+19x^48+8x^49+11x^50+2x^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 6.72 seconds.