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

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

Homogenous weight enumerator: w(x)=1x^0+135x^36+368x^38+438x^40+32x^42+49x^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 0.043 seconds.