The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^35+279x^36+564x^37+1316x^38+2676x^39+4855x^40+7600x^41+9809x^42+10820x^43+10268x^44+7962x^45+4709x^46+2448x^47+1181x^48+494x^49+278x^50+112x^51+53x^52+18x^53+14x^54+4x^55+3x^56+2x^57+1x^58+1x^62

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 28.4 seconds.