Anovan: within-subjects anova with covariate and random factor is rank-deficient

I am currently analysing a dataset that has one dependent variable (Y), two within-subject factors with two levels each (A, B with levels a1,a2,b1,b2) and a covariate C.

For arguments sake, let's say that I measure my subjects' happiness (Y) after they each eat Western or Eastern Food ( Factor A) that can each be Spicy or Sweet ( Factor B). As Covariate, I include their age. I read that anovan can run within-subject ANOVA if you take into account the subject's identity as a random variable, which gives the final column Subject. This can be summarised as follows:

if true

|   Y   |   A   |   B   |  Cov  |   Subject   |
_______________________________________________
|   1   |   0   |   0   |   20  |   1         |
|   5   |   1   |   0   |   20  |   1         |
|   3   |   1   |   1   |   20  |   1         |
|   8   |   0   |   1   |   20  |   1         |
|   2   |   0   |   0   |   23  |   2         |
|   4   |   1   |   0   |   23  |   2         |
|   4   |   1   |   1   |   23  |   2         |
|   7   |   0   |   1   |   23  |   2         |
_______________________________________________

end

If I understand correctly, I can run a within-subject ANOVA in MATLAB by using anovan and then including the subject's identity as random factor:

if true
  anovan(Y,{A B Subject},'random',3)
end

This does indeed return results that seem reasonable. However if I want to include the covariate I run into a problem:

if true
  anovan(Y,{A B Subject Cov},'random',3,'continuous',4)
end

The problem is that if I include both the covariate as well as the subject's identity, my ANOVA design is rank deficient. Is there any way in MATLAB to work around this?