The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+240x^35+468x^36+1376x^37+2259x^38+4868x^39+6813x^40+11580x^41+10080x^42+11920x^43+7005x^44+4838x^45+2044x^46+1252x^47+418x^48+242x^49+76x^50+24x^51+15x^52+10x^53+5x^54+2x^57

The gray image is a code over GF(2) with n=336, k=16 and d=140.
This code was found by Heurico 1.16 in 27.4 seconds.