The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  0  2  0  1  2  1  4  1  1  1  1  1 12  0  1  2  1  1  2  0  1
 0  2  0  6  0  6  8  6 14  0  0 14  6  4 12 10  4  2 14  2  6  2  6  2 14  2  2  2  4  4  4  4 12  2  0  6  2 12  4 14  2  0
 0  0 12  0  0  0 12  0  0  8  4  4  4  4  8  4 12  8  0  4  8  4 12  0  4 12  4 12  8  8  8  8  4  0  4  8  0 12  4  0 12  0
 0  0  0 12  0  0  0  4  8 12  4 12  0  0  8 12  8  0  8  4  8  8 12 12  0 12  4  8 12  4 12  8 12  4  8  4 12 12  0 12  0  0
 0  0  0  0 12  0  4  4 12  4  0  4  4  8 12  0 12  4  4 12  0  4  8  4  8  4  8  0  4  0  4  8  0  4  8  0  8 12  0  0  4  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  8  0  0  8  0  8  8  8  0  0  0  8  0  8  8  0  0  0  8  8  0  8  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+53x^34+94x^35+235x^36+432x^37+599x^38+1194x^39+1846x^40+2414x^41+2773x^42+2340x^43+1804x^44+1228x^45+613x^46+378x^47+173x^48+70x^49+52x^50+26x^51+37x^52+16x^53+4x^54+2x^58

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 3.26 seconds.