The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^32+36x^33+234x^34+332x^35+1348x^36+1796x^37+2946x^38+2860x^39+3014x^40+1740x^41+1246x^42+388x^43+251x^44+12x^45+54x^46+4x^47+27x^48+8x^52+2x^56+1x^60

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 1.85 seconds.