Find elements of $\{0,1\}^4$

Question

For a classroom repartition problem, I need to find a multiset of 8 vectors among $\{0,1\}^4$ such that

1. Multiset: A vector can be present several times in the multiset
2. Their sum with the regular addition is $[4, 4, 4, 4]$
3. If a vector is in the multiset, its complementary is not in the multiset
4. (optional) We want to minimize the uniformity, defined by the squared sum of all (cross-products with the XOR operation, minus 2). For example the uniformity of the multiset $\{[0, 0, 1, 1], [0, 0, 0, 0]\}$ is $0$, whereas the uniformity of the multiset $\{[0, 0, 0, 0], [0, 0, 0, 0]\}$ is 4 and the uniformity of the multiset $\{[1, 1, 1, 1], [0, 0, 0, 0]\}$ is 4

I just can't even find a solution for the basis case 1. and 2. If 2. is not possible, I want a proof and minimize how many of these vectors/complementary we need.

For example, here is a solution but the problem is that there are two complementary vectors [0, 1, 1, 1] and [1, 0, 0, 0]

[0, 0, 0, 0]
[1, 0, 0, 1]
[0, 1, 1, 1]
[1, 1, 1, 0]
[0, 0, 0, 1]
[1, 0, 0, 0]
[0, 1, 1, 1]
[1, 1, 1, 0]

Answer 1

I'm not sure what (4) means, but to satisfy (2) and (3):

[1111], [1111], [1100], [1010], [0100], [0010], [0001], [0001]