Given, (1+x+x^2+x^3)^11.

To find the coefficient of x^4, we need to find the number of ways in which x^4 can be obtained by multiplying the terms in the expansion.

Let's consider the powers of x that can be obtained by multiplying the terms in the expansion:

0 (when none of the terms are multiplied)

1 (when one of the terms is multiplied)

2 (when two of the terms are multiplied)

3 (when three of the terms are multiplied)

4 (when four of the terms are multiplied)

We need to find the number of ways in which we can get a power of x equal to 4.

The maximum power of x in each term is 3. Therefore, we can only get a power of 4 by multiplying one term with power 1 and another term with power 3.

The number of ways in which we can choose one term with power 1 and another term with power 3 is:

11C1 * 10C1 = 110

We need to multiply this by the coefficient of the term (x^1 * x^3) in the expansion of (1+x+x^2+x^3)^11.

The coefficient of the term (x^1 * x^3) is the same as the coefficient of x^2 in the expansion of (1+x+x^2+x^3)^11.

To find the coefficient of x^2, we can use the multinomial theorem:

The coefficient of x^2 in the expansion of (1+x+x^2+x^3)^11 is:

(11+2-1)C(2,2,7,0) = 12C2 = 66

Therefore, the coefficient of x^4 is:

110 * 66 = 7260

But we need to divide this by 4! (4 factorial) to get the coefficient of x^4:

7260/24 = 303

Therefore, the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is 303, which is option D.