The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^36+508x^37+996x^38+1618x^39+2927x^40+4362x^41+7095x^42+9598x^43+10755x^44+9702x^45+7534x^46+4476x^47+2730x^48+1486x^49+847x^50+412x^51+198x^52+86x^53+38x^54+4x^55+4x^56+2x^59+1x^60+2x^62+2x^63

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 seconds.