The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^35+149x^36+310x^37+416x^38+670x^39+1193x^40+2102x^41+3459x^42+5034x^43+5976x^44+5074x^45+3461x^46+2166x^47+1189x^48+642x^49+370x^50+230x^51+119x^52+64x^53+34x^54+36x^55+9x^56+3x^58+4x^60+1x^62

The gray image is a code over GF(2) with n=352, k=15 and d=140.
This code was found by Heurico 1.16 in 13.1 seconds.