The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+156x^32+518x^33+1158x^34+2336x^35+4548x^36+7120x^37+11151x^38+11786x^39+10821x^40+7250x^41+4722x^42+2202x^43+1010x^44+452x^45+179x^46+70x^47+40x^48+4x^49+6x^50+6x^51

The gray image is a code over GF(2) with n=312, k=16 and d=128.
This code was found by Heurico 1.16 in 24.8 seconds.