Bash + Unix utilities, 29 bytes

dc -e2o8800979740570p|fold -4

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Pure Bash, 34 bytes

echo 0{0,1}{0,1}{0,1} 10{00,01,10}

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Bash + Unix utilities, 29 26 bytes

dc -e2o8927II^*8/p|fold -4

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This is the same length as @DigitalTrauma/@Dennis's solution, but uses a completely different method.

Output is:

1010
0010
0110
0001
1001
0101
0100
0111
0011
1000
0000

(Any order is allowed.)

Pure Bash, 34 bytes

echo 0{0,1}{0,1}{0,1} 10{00,01,10}

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Output is:

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010

Pure Bash, 34 bytes

echo 0{0,1}{0,1}{0,1} 10{00,01,10}

Try it online!

Bash + Unix utilities, 29 bytes

dc -e2o8800979740570p|fold -4

Try it online!

Pure Bash, 34 bytes

echo 0{0,1}{0,1}{0,1} 10{00,01,10}

Try the pure Bash version online!