vim, 120 bytes

Result

WA

Code [DL]

00000000  71 7a 22 61 78 22 62 78  22 63 78 22 64 78 22 65  |qz"ax"bx"cx"dx"e|
00000010  78 22 66 78 22 67 78 22  68 73 12 3d 28 40 61 2a  |x"fx"gx"hs.=(@a*|
00000020  31 32 38 2b 40 62 2a 36  34 2b 40 63 2a 33 32 2b  |128+@b*64+@c*32+|
00000030  40 64 2a 31 36 2b 40 65  2a 38 2b 40 66 2a 34 2b  |@d*16+@e*8+@f*4+|
00000040  40 67 2a 32 2b 40 68 29  2a 38 2b 31 0a 1b 63 63  |@g*2+@h)*8+1..cc|
00000050  12 3d 70 6f 77 28 66 6c  6f 6f 72 28 73 71 72 74  |.=pow(floor(sqrt|
00000060  28 40 40 29 29 2c 32 29  3d 3d 40 40 0a 1b 6a 5e  |(@@)),2)==@@..j^|
00000070  71 34 39 40 7a 5a 5a 0a                           |q49@zZZ.|
00000078

Disassembly

qz"ax"bx"cx"dx"ex"fx"gx"hs<C-R>=(@a*128+@b*64+@c*32+@d*16+@e*8+@f*4+@g*2+@h)*8+1<NL><Esc>cc<C-R>=pow(floor(sqrt(@@)),2)==@@<NL><Esc>j^q49@zZZ<NL>

stdin

11101110
00001111
11101001
10011001
01111111
00100100
11000111
00000001
01000110
11100111
00001010
00100110
00010000
00000110
01001100
10010101
11111111
01100100
01100111
00001100
00101101
00101001
01000010
11111101
11111000
11000101
11010010
01011011
00011010
11100111
00111000
11010010
10101011
00110000
10000101
01111000
00000000
01000111
10011110
10111110
00000011
10000100
01101001
11011011
01001110
00010101
00010001
00011100
00110111
10001000

stdout

11101110
00001111
11101001
10011001
01111111
00100100
11000111
00000001
01000110
11100111
00001010
00100110
00010000
00000110
01001100
10010101
11111111
01100100
01100111
00001100
00101101
00101001
01000010
11111101
11111000
11000101
11010010
01011011
00011010
11100111
00111000
11010010
10101011
00110000
10000101
01111000
00000000
01000111
10011110
10111110
00000011
10000100
01101001
11011011
01001110
00010101
00010001
00011100
00110111
10001000

stderr

strace