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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+68x^39+85x^40+236x^41+301x^42+208x^43+38x^44+48x^45+17x^46+12x^47+4x^48+4x^49+1x^50+1x^78

The gray image is a code over GF(2) with n=336, k=10 and d=156.
This code was found by Heurico 1.16 in 24.9 seconds.