Sort raw data from a stream, with more zeros on top

I have raw data from a stream, the data is represented like the following N*13 matrix:

%       Z            Data      dE  
% _____________  ___________  _____
%  0 0 0 0 0 0   1 2 3 5 2 6   1.0 
%  2 1 0 9 0 0   2 5 9 1 8 6   1.5
%  0 0 4 0 0 0   1 2 2 5 9 4   2.0
%  0 0 7 0 1 6   1 6 3 5 1 6   0.1
%  0 0 3 0 1 6   1 2 3 5 7 6   0.4

Rows for whole matrix must be sorted like this:

1. Priority to Z, by number of zeros in a descending order (more zeros on top)
2. If two lines have same number of zeros in Z, lowest dE has priority (on top)

Considering the example above order should be: 1,3,4,5,2

Answer 1

[Guillaume]

numzeros = sum(yourmatrix(:, 1:6) == 0, 2);
[~, order] = sortrows([numzeros, yourmatrix(:, 13)], [-1 2]);
yourmatrix = yourmatrix(order, :)

Answer 2

[dpb]

>> [~,ix]=sortrows([sum(Z==0,2) dE],[-1 2])
ix =
   1
   3
   4
   5
   2
>>