The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^34+96x^35+219x^36+332x^37+628x^38+1076x^39+1818x^40+2630x^41+2769x^42+2606x^43+1853x^44+1002x^45+608x^46+346x^47+179x^48+58x^49+40x^50+34x^51+23x^52+10x^53+4x^54+2x^55+2x^56+1x^58+1x^60

The gray image is a code over GF(2) with n=336, k=14 and d=136.
This code was found by Heurico 1.16 in 3.25 seconds.