Bruteforce

vector<int> vCoeffs;

void Recursive(int nLvl)
{
    if (vCoeffs[nLvl] == 3)
    {
        vCoeffs[nLvl] = 0;
        return;
    }

    for (int i = nLvl + 1; i < (int)vCoeffs.size(); i++)
        Recursive(i);

    vCoeffs[nLvl]++;

    for (int i = 0; i < (int)vCoeffs.size(); i++)
        printf("%d ", vCoeffs[i]);

    printf("\n");

    Recursive(nLvl);
}

int main()
{
    for (int i = 0; i < 4; i++)
        vCoeffs.push_back(0);

    Recursive(0);

    _getch();
    return 0;
}



//--------------------- THE RESULT -------------------------
/8
0 0 0 1
0 0 0 2
0 0 0 3
0 0 1 0
0 0 1 1
0 0 1 2
0 0 1 3
0 0 2 0
0 0 2 1
0 0 2 2
0 0 2 3
0 0 3 0
0 0 0 1
0 0 0 2
0 0 0 3
0 1 0 0
0 1 0 1
0 1 0 2
0 1 0 3
0 1 1 0
0 1 1 1
0 1 1 2
0 1 1 3
0 1 2 0
0 1 2 1
0 1 2 2
0 1 2 3
0 1 3 0
0 1 0 1
0 1 0 2
0 1 0 3
0 2 0 0
0 2 0 1
0 2 0 2
0 2 0 3
0 2 1 0
0 2 1 1
0 2 1 2
0 2 1 3
0 2 2 0
0 2 2 1
0 2 2 2
0 2 2 3
0 2 3 0
0 2 0 1
0 2 0 2
0 2 0 3
0 3 0 0
0 0 0 1
0 0 0 2
0 0 0 3
0 0 1 0
0 0 1 1
0 0 1 2
0 0 1 3
0 0 2 0
0 0 2 1
0 0 2 2
0 0 2 3
0 0 3 0
0 0 0 1
0 0 0 2
0 0 0 3
1 0 0 0
1 0 0 1
1 0 0 2
1 0 0 3
1 0 1 0
1 0 1 1
1 0 1 2
1 0 1 3
1 0 2 0
1 0 2 1
1 0 2 2
1 0 2 3
1 0 3 0
1 0 0 1
1 0 0 2
1 0 0 3
1 1 0 0
1 1 0 1
1 1 0 2
1 1 0 3
1 1 1 0
1 1 1 1
1 1 1 2
1 1 1 3
1 1 2 0
1 1 2 1
1 1 2 2
1 1 2 3
1 1 3 0
1 1 0 1
1 1 0 2
1 1 0 3
1 2 0 0
1 2 0 1
1 2 0 2
1 2 0 3
1 2 1 0
1 2 1 1
1 2 1 2
1 2 1 3
1 2 2 0
1 2 2 1
1 2 2 2
1 2 2 3
1 2 3 0
1 2 0 1
1 2 0 2
1 2 0 3
1 3 0 0
1 0 0 1
1 0 0 2
1 0 0 3
1 0 1 0
1 0 1 1
1 0 1 2
1 0 1 3
1 0 2 0
1 0 2 1
1 0 2 2
1 0 2 3
1 0 3 0
1 0 0 1
1 0 0 2
1 0 0 3
2 0 0 0
2 0 0 1
2 0 0 2
2 0 0 3
2 0 1 0
2 0 1 1
2 0 1 2
2 0 1 3
2 0 2 0
2 0 2 1
2 0 2 2
2 0 2 3
2 0 3 0
2 0 0 1
2 0 0 2
2 0 0 3
2 1 0 0
2 1 0 1
2 1 0 2
2 1 0 3
2 1 1 0
2 1 1 1
2 1 1 2
2 1 1 3
2 1 2 0
2 1 2 1
2 1 2 2
2 1 2 3
2 1 3 0
2 1 0 1
2 1 0 2
2 1 0 3
2 2 0 0
2 2 0 1
2 2 0 2
2 2 0 3
2 2 1 0
2 2 1 1
2 2 1 2
2 2 1 3
2 2 2 0
2 2 2 1
2 2 2 2
2 2 2 3
2 2 3 0
2 2 0 1
2 2 0 2
2 2 0 3
2 3 0 0
2 0 0 1
2 0 0 2
2 0 0 3
2 0 1 0
2 0 1 1
2 0 1 2
2 0 1 3
2 0 2 0
2 0 2 1
2 0 2 2
2 0 2 3
2 0 3 0
2 0 0 1
2 0 0 2
2 0 0 3
3 0 0 0
*/