The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^36+164x^37+162x^38+280x^39+179x^40+108x^41+44x^42+16x^43+4x^44+8x^45+1x^46+1x^70

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 0.0408 seconds.