The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+127x^34+152x^35+740x^36+828x^37+2772x^38+4444x^39+8033x^40+9980x^41+11527x^42+9868x^43+8000x^44+4436x^45+2825x^46+884x^47+583x^48+116x^49+145x^50+12x^51+44x^52+10x^54+7x^56+1x^58+1x^62

The gray image is a code over GF(2) with n=336, k=16 and d=136.
This code was found by Heurico 1.16 in 29.4 seconds.