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  1  2  1  1  1  4  0  1  1  1  2  1  1  2  2  4  0  4  1  1
 0  2  0  6  0  6  8  6 14  0  0 14  6  4 12 10  4  2 14  2  6  2  6  4  2 14  8 10  2  2  6  4  8 14  0  2  6  6  0  8  2 10  0
 0  0 12  0  0  0 12  0  0  8  4  4  4  4  8  4 12  8  0  4  8  4 12  8 12  4  0 12 12 12  4  0 12  4  4  0  8  8  8  8  0  8  8
 0  0  0 12  0  0  0  4  8 12  4 12  0  0  8 12  8  0  8  4  8  8 12 12 12  0  8 12  8 12  4  4  4  8  0  8 12  8 12  4  0  8  0
 0  0  0  0 12  0  4  4 12  4  0  4  4  8 12  0 12  4  4 12  0  4  8  8  4  8  0  0  0  8 12 12  8  8  0 12 12  0 12 12  4  0  8
 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  8  0  8  0  8  0  0  0  8  8  8  8  8  0  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+44x^35+98x^36+210x^37+438x^38+798x^39+1202x^40+1734x^41+2388x^42+2608x^43+2409x^44+1826x^45+1147x^46+716x^47+342x^48+178x^49+103x^50+52x^51+41x^52+20x^53+19x^54+6x^55+3x^56+1x^58

The gray image is a code over GF(2) with n=344, k=14 and d=140.
This code was found by Heurico 1.16 in 3.45 seconds.