The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1  4  1  1  1  6  1  1  8  1  1  0  1  8  0  1  1  0  1  1  1  1  2  4  1  1  1 12  1  1  1  1
 0  1 11  6  1  1  8 11  1 13  6  1 10  1 11  1  0  1  5  2  1  8  4  1  3  1  1 15  4  1  6 14  9  1  1  1  1  8  9  2 13 10  0  0
 0  0 12  0  0  0  0  0  8  4  4  4  4  8  4  8  0  0 12 12  8 12 12  4  4  4 12  0  0 12  4  8 12  0 12  4  0 12  8 12  8 12 12  0
 0  0  0 12  0  0 12  8 12  0  0 12  0  4  4 12  4 12  8  0  8 12  8 12 12  8  8  8  0  8  4  4  8  0 12 12 12  4  8 12  0  4  0  8
 0  0  0  0  4  0  8  4  0  8  4 12 12  0  4  8  4  4 12  8 12  4  0  0  8  4  8  8 12  4  8 12 12 12  4 12 12 12 12  0  4  0 12  8
 0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  0  0  8  8  8  8  0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  0  0  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+38x^36+140x^37+251x^38+524x^39+1122x^40+2048x^41+3898x^42+5482x^43+5778x^44+5538x^45+3943x^46+2054x^47+1062x^48+414x^49+201x^50+118x^51+59x^52+50x^53+26x^54+14x^55+3x^56+2x^57+1x^58+1x^60

The gray image is a code over GF(2) with n=352, k=15 and d=144.
This code was found by Heurico 1.16 in 8.39 seconds.