The generator matrix

 1  0  1  1  1  6  1 12  1  1 14  1  1  1  8 14  1  1  1  0  1  1  8  1  2  1  4  1  1  1  1  1  1  2  1 12  2  2  1
 0  1 11  6 13  1  8  1 11 13  1  6 12  1  1  1  7  6  2  1  3  5  1  4  1 15  1 12  5 12 15  4  5  0 15  1 12  8  0
 0  0 12  0  4  0  0  8  8  0  8  0  0  8  4 12  4 12  4 12 12  4  0  4  8 12  4  4 12  8  0  8 12  4  4  4  4  0  0
 0  0  0 12  0  0  4  8 12  4 12  8  8  4  0  8  0  4  8  4  4  4  4  8 12  4  8 12 12  0  0 12  4 12  4 12  4  4  0
 0  0  0  0  8  0  8  8  8  0  8  0  8  0  0  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  8  0  0  0  8  0  8  8  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  0  8  0  8  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+51x^32+84x^33+311x^34+368x^35+1361x^36+1566x^37+3125x^38+2680x^39+3175x^40+1494x^41+1385x^42+384x^43+253x^44+42x^45+37x^46+24x^47+17x^48+14x^49+4x^50+6x^52+2x^54

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 1.82 seconds.