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Consider the following, which works:

sage: R.<x> = Integers(4)[]
sage: Q.<a> = R.quotient(x^2)
sage: for q in Q:
....:     q
....:     
0
1
2
3
a
a + 1
a + 2
a + 3
2*a
2*a + 1
2*a + 2
2*a + 3
3*a
3*a + 1
3*a + 2
3*a + 3

Now if I add a generator to the ideal and execute

sage: Q.<a> = R.quotient((x^2,2*x))
sage: for q in Q:
....:     q
....:

I get an error:

NotImplementedError: object does not support iteration

How can I make it work?

Consider the following, which works:

sage: R.<x> = Integers(4)[]
sage: Q.<a> = R.quotient(x^2)
sage: for q in Q:
....:     q
....:     
0
1
2
3
a
a + 1
a + 2
a + 3
2*a
2*a + 1
2*a + 2
2*a + 3
3*a
3*a + 1
3*a + 2
3*a + 3

Now if I add a generator to the ideal (which should yield a quotient with 8 elements) and execute

sage: Q.<a> = R.quotient((x^2,2*x))
sage: for q in Q:
....:     q
....:

I get an error:

NotImplementedError: object does not support iteration

How can I make it work?

Consider the following, which works:

sage: R.<x> = Integers(4)[]
sage: Q.<a> = R.quotient(x^2)
sage: for q in Q:
....:     q
....:     
0
1
2
3
a
a + 1
a + 2
a + 3
2*a
2*a + 1
2*a + 2
2*a + 3
3*a
3*a + 1
3*a + 2
3*a + 3

Now if I add a generator to the ideal (which should yield a quotient with 8 elements) and execute

sage: Q.<a> = R.quotient((x^2,2*x))
sage: for q in Q:
....:     q
....:

, which should yield a quotient with 8 elements, I get an error:

NotImplementedError: object does not support iteration

How can I make it work?

Consider the following, which works:

sage: R.<x> = Integers(4)[]
sage: Q.<a> = R.quotient(x^2)
sage: for q in Q:
....:     q
....:     
0
1
2
3
a
a + 1
a + 2
a + 3
2*a
2*a + 1
2*a + 2
2*a + 3
3*a
3*a + 1
3*a + 2
3*a + 3

Now if I add a generator to the ideal and execute

sage: Q.<a> = R.quotient((x^2,2*x))
sage: for q in Q:
....:     q
....:

, which should yield a quotient with 8 elements, I get an error:

NotImplementedError: object does not support iteration

How can I make it work?

Consider the following, which works:

sage: R.<x> = Integers(4)[]
sage: Q.<a> = R.quotient(x^2)
sage: for q in Q:
....:     q
....:     
0
1
2
3
a
a + 1
a + 2
a + 3
2*a
2*a + 1
2*a + 2
2*a + 3
3*a
3*a + 1
3*a + 2
3*a + 3

Now if I add a generator to the ideal and execute

sage: Q.<a> = R.quotient((x^2,2*x))
sage: for q in Q:
....:     q
....:

which should yield a quotient with 8 elements, I get an error:

NotImplementedError: object does not support iteration

How can I make it work?work? Sage doesn't seem to be able to deal with finite rings that aren't principal ideal rings.