The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+101x^36+312x^38+256x^39+266x^40+40x^42+47x^44+1x^72

The gray image is a code over GF(2) with n=312, k=10 and d=144.
This code was found by Heurico 1.16 in 0.0532 seconds.