The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  1  0 14  1  1  1  1  8 10  1  1  1  1  1  8  1  1  6  1  1  1  1  1  8  1  2  2  0  1  8  1
 0  1 11  6  1  1  8  5  1  3  1  6  7 14  1  1  0  5 11  0  1  1 14  3  6  3  7  1 13  7  1  8  8 14  1  2  0  9  8  1  1 11  1  0
 0  0 12  0  0  0  0  0  0  0  0  8  0 12 12  4  4 12  4  4  4 12  4 12  8 12  4  8  8  0  0 12 12  8  8  4  0  8  4  8  0 12 12  8
 0  0  0 12  0  0  0  0  4  4 12 12 12  0  4  0  4  4  4  8 12  8  4  8  4  8  4  4  8  4  8  4  8 12  4  0  4 12  0  0  4 12  0  8
 0  0  0  0  4  0  8  4  0  4  0  0  4  4 12 12  4  8  0 12 12 12  4  0  8  0  8 12  8  8  4  8  8 12  0  8  4  8  8  4  4  8  8  8
 0  0  0  0  0 12 12  4 12  8  8  4 12  4 12  4  4  0 12  8  8  8  0  4 12  0  4 12 12  8  4  4 12 12  8  0  0  4  8  0  8 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+54x^35+138x^36+276x^37+449x^38+1272x^39+2234x^40+4932x^41+7166x^42+10700x^43+10645x^44+11228x^45+7511x^46+4832x^47+1932x^48+1164x^49+474x^50+270x^51+113x^52+64x^53+43x^54+24x^55+9x^56+4x^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 31.5 seconds.