Just curious why you would want to do this? I mean, Cross product arrays are a fantastic idea for robust design, but a 4level factor? Is the 4level factor continuous or categorical? While I know there are a number of 2level orthogonal arrays, Taguchi, philosophically, suggests 3level designs for the design factors (he doesn't really believe relationships are linear). Also for the outer array, since you will have to have 4 combinations (3 DFs) you might as well add a third noise variable for the 3rd DF since you don't care about noisebynoise interactions.
To the best of my recollection (this was a long time ago), the way Taguchi did it was to take three columns from the orthogonal array (3 DFs, same for a 4level factor). That will give you 8 possible combinations. Set those to 4 levels like this:
A 
B 
C 

D 
1 
1 
1 

1 
1 
1 
1 

2 
1 
1 
1 

3 
1 
1 
1 

4 
1 
1 
1 

1 
1 
1 
1 

2 
1 
1 
1 

3 
1 
1 
1 

4 
Don't use the 3 columns used to create the 4 level factor (obviously). But I could be completely wrong...LOL
"All models are wrong, some are useful" G.E.P. Box