The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+418x^39+770x^40+846x^41+572x^42+466x^43+379x^44+314x^45+187x^46+116x^47+9x^48+16x^49+1x^52+1x^54

The gray image is a code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.16 in 0.166 seconds.