That presentation seems to be pretty much what I have written. I guess someone copied that and some other copied the second guy and I just copied the third guy.

Sorry for not showing the code. I haven't realized that grassmannOps.m is not longer on the web... Anyway, I found the problem: when defining $\mathcal D\mathcal D[\{x,y\},\{i,j\}]=\epsilon^{\alpha\,\beta}\mathcal D[x,\{\alpha,i\}]**\mathcal D[y,\{\beta,j\}]$ GD do something funny with the term inside the bracket {x,y}. To solve the issue I have to define my derivative square as $\mathcal D\mathcal D[x,y,\{i,j\}]=\epsilon^{\alpha\,\beta}\mathcal D[x,\{\alpha,i\}]**\mathcal D[y,\{\beta,j\}]$ And that's it.