The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+186x^35+477x^36+1066x^37+1709x^38+3012x^39+4243x^40+7930x^41+8406x^42+11452x^43+8352x^44+7944x^45+4579x^46+3074x^47+1419x^48+946x^49+391x^50+190x^51+95x^52+34x^53+16x^54+6x^55+5x^56+3x^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 41.5 seconds.