The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1 12  1  1  1 10  4  1  1  1  1  2  0  6  4  2  4  6  6  4 12  1  1  1  1 12  4
 0  1 11  6  5  1  9  8  1  7 14  1  4  1 13 10  3  1  1 12 15  2  1  1  1  1  1  1  1  1  1  1  1  0 13  0 13  1  4
 0  0 12  0  8  0  8  4 12  4 12  4  4  0 12  8  0  8 12  8  0 12  4  4  8  8  4  4  8  0 12 12  4  0 12 12  0  0 12
 0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  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+303x^36+208x^37+408x^38+256x^39+417x^40+144x^41+248x^42+32x^43+25x^44+4x^48+2x^56

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 1.08 seconds.