The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+108x^35+94x^36+270x^37+362x^38+448x^39+362x^40+206x^41+50x^42+84x^43+22x^44+34x^45+2x^46+1x^48+2x^49+1x^50+1x^66

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 39.9 seconds.