The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+224x^36+436x^37+1051x^38+1608x^39+3197x^40+4484x^41+7216x^42+8792x^43+11336x^44+8908x^45+7486x^46+4536x^47+3134x^48+1484x^49+876x^50+424x^51+206x^52+48x^53+71x^54+11x^56+4x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=352, k=16 and d=144.
This code was found by Heurico 1.16 in 41.1 seconds.