The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^32+456x^33+894x^34+2132x^35+4601x^36+7498x^37+10790x^38+12584x^39+11106x^40+7550x^41+4358x^42+2132x^43+870x^44+358x^45+74x^46+48x^47+11x^48+10x^49+12x^50+9x^52

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 19.6 seconds.