# Complete Intersection ideal whose initial ideal is not even Cohen-Macaulay

I am trying to find an example, such a example is asked in exercise 3.3 of the book Monomial Ideals (Herzog & Hibi).

I would like to find a graded ideal $$I\subset k[x_1,\cdots,x_n]$$ which is complete intersection, but $$\mbox{In}_<(I)$$ is not even Cohen-Macaulay (for some monomial order $$<$$).

I would be happy with any hint.

PS: I'm trying to find a example using Singular and Macaulay2, but until to now I got nothing .