The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  1  0  1  1  2  1  8  1  0  1  4  4  1  2  1 12  4  4  8  1
 0  2  0  2  0  0  6  6  4  4 10  6 14  4  8  2  4  4  6 12  2  4 14 10  0  2  4  0  6  2  4  2  2 10  8  2  2  4  4
 0  0  2  2 12  6  6  0 12  2 14 12  2 12 10  4  2  2  0  0  8 14 12  6  4  2 14  2  2 12  2  2 10 10  2 10 10  2  2
 0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  8  0  0  0  8  8  8  8  8  0  8  8  8  8  8  0  0  8  8  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  0  0  0  8  8  0  0  8  0  8  8  8  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  0  0  8  0  0  8  0  8  8  8  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+62x^32+222x^33+307x^34+882x^35+904x^36+2304x^37+1756x^38+3470x^39+1882x^40+2296x^41+930x^42+846x^43+208x^44+152x^45+60x^46+50x^47+15x^48+18x^49+19x^50

The gray image is a code over GF(2) with n=312, k=14 and d=128.
This code was found by Heurico 1.16 in 2.56 seconds.