The generator matrix

 1  0  0  1  1  1  6  4  1  1  1  4  2  1  1  1  1 12  2  1  1  1  1 10 10  8  0  1  1  1 12  1  1  1  8 10  1 12  1
 0  1  0  2  5  7  1  1  4  1 11  6  1  0 15 14  8  1  4  3 10 12  4 10  1  0  1  3  5  0  1  2 11  8  1 14  6  1  0
 0  0  1  1  3 10  3  7  6  4  3  1  2  5  4  0  7  2  1  3  6 15 10  1  7  1  5 13 13  5  6 11  3 13 15  1  0  9  0
 0  0  0  4  0  4  0  8  4  8  4  4  8  8 12  4  8 12  0  8  0 12  0  4 12 12  8  4  0  8  4  8  8  4  8  8  4 12  8
 0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  8  0  0  0  8  8  8  0  8  8  0  8  8  8  0  8  8  8  8  0  8
 0  0  0  0  0  8  8  0  0  8  0  0  8  0  8  8  8  8  0  8  8  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  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+53x^32+330x^33+920x^34+2314x^35+4481x^36+7796x^37+10915x^38+11910x^39+11007x^40+7912x^41+4444x^42+2106x^43+831x^44+332x^45+96x^46+50x^47+11x^48+14x^49+8x^50+4x^51+1x^54

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 20.2 seconds.