The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+60x^35+324x^36+536x^37+1258x^38+2232x^39+4924x^40+7128x^41+10768x^42+10802x^43+11165x^44+7266x^45+4864x^46+2100x^47+1192x^48+460x^49+250x^50+94x^51+55x^52+34x^53+10x^54+8x^55+3x^56+2x^58

The gray image is a code over GF(2) with n=344, k=16 and d=140.
This code was found by Heurico 1.16 in 28.7 seconds.