I think what you are looking for is **mixed codes**.

A good start point would be [Brouwer--Hämäläinen--Östergård--Sloane](http://www.ams.org/mathscinet-getitem?mr=1486654). They are talking about mixed binary/ternary code, so for some $k$, $n_1=\cdots=n_k=2$ while $n_{k+1}=\cdots=n_N=3$.  Brouwer keep an [online list of known 3/2 mixed code](http://www.win.tue.nl/~aeb/codes/23codes.html).  I think they also talked about some general cases.

Another interesting paper is [Perkins--Sakhonivich--Smith](http://www.ams.org/mathscinet-getitem?mr=2236184).  It seems to be initially cited as "mixed codes: bounds, constructions and some applications" before publication, which confused me. Fujiwara also find this reference.

Anyway, more papers can be found from the references therein or by the key word.  I also find [this online list](http://www.sztaki.hu/~keri/codes/) with 4/3/2 mixed covering codes and many references.

**update**: Turbo mentioned a work of [Lenstra](http://www.ams.org/mathscinet-getitem?mr=878574) in the comment.  It already uses the term "mixed codes" on the first page.