The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 12  1  1  6  1  2  2  1  1  1  1  1 10  1  1  0  1  0  1
 0  1  3  6  5  1 15 12  1 10  9  1  0  3  1  6  5  1 12 15  1  6  5  1 10  0 12 14 12  4 10  9  1 12  3  1 15  1  0
 0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  0  8  0  0  8  0
 0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  0  8  0  0  8  8  0  8  8  0  0  0  8  8  8  8  0
 0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  0  8  0  8  8  0  8  8  0  0  8  0  0  0  0  0  8  8  8  0  0  8

generates a code of length 39 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+48x^35+194x^36+304x^37+272x^38+400x^39+341x^40+272x^41+124x^42+64x^43+20x^44+4x^46+1x^48+2x^52+1x^56

The gray image is a code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 0.0508 seconds.