The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  0  2  1  1  1  1  2  2  8  2  1  1  1  0  1  2  1  8  1  2  1  4
 0  2  0  6  0  6  8  2  4  6  4 10 14  2  0 14  2  2 14  8  6 14 10  6 14  2  6 10  0  4  2  0  2 14  4  6 12  4  8
 0  0 12  0  0  0 12  0 12  0  4  8  0  8  8 12 12  4  4  8  4  4 12  0  8  8  0  4  0  0  0 12 12  8  8  4  4  0  0
 0  0  0 12  0  0  0  4  8  4  8 12  8  8 12  0  0  4 12 12  4 12  8  8  4  0  4  8 12  8  8 12  8  8  0  4  8 12  8
 0  0  0  0 12  0  4  8  0  4  4 12 12 12  4  8  4  8 12  0  8  4 12  0  8 12 12  8 12  4  0  0  0  4 12 12  8  0 12
 0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0  8  8  8  0  0  8  0  8  0  8  0  0  0  0  8  0  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+157x^32+124x^33+468x^34+604x^35+1192x^36+1956x^37+2346x^38+2828x^39+2307x^40+1956x^41+1072x^42+596x^43+421x^44+124x^45+162x^46+4x^47+47x^48+16x^50+3x^52

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 3.09 seconds.