The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+78x^35+276x^36+412x^37+961x^38+1326x^39+2727x^40+3952x^41+7387x^42+9686x^43+12016x^44+9372x^45+7634x^46+4202x^47+2649x^48+1200x^49+827x^50+364x^51+272x^52+96x^53+52x^54+24x^55+11x^56+8x^57+2x^58+1x^62

The gray image is a code over GF(2) with n=352, k=16 and d=140.
This code was found by Heurico 1.16 in 44.3 seconds.