The generator matrix

 1  0  0  1  1  1 10  2  1  1  1 14  1  8  1  1  0 14  1 12  1 10  6  1  1 10  1  4  1  8  1  2  1  2 10  1  1  1  1
 0  1  0  8  5 13  1  1 14 11 12 12  3  1  6  9  6  1  4  1  2  2  1  3  5 12  9  1  9 12 14  6 15  1  1 11  2 12  1
 0  0  1 11  3  8 15  2 15  7  2  1 10 13 13 14  1 12  9 10  4  1  9 12  1  1  4 11 13  1  3  1  1 14 11  6 15  0  3

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

Homogenous weight enumerator: w(x)=1x^0+294x^36+900x^37+748x^38+752x^39+423x^40+432x^41+208x^42+192x^43+104x^44+28x^45+12x^46+2x^48

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 0.112 seconds.