You can do one thing. Use the first string as it is for the rest of the 9 strings except randomly generate an index (between 1 to n) and assign a random integer only to that positions with that random index.
population(1,:) = [100 110 120 130 140 150 160 170 180 190];
for i = 2:10
idx = randi([1 10]);
population(i,:) = population(1,:);
population(i,idx) = randi([0 255]);
end
With this you will get ten strings differing in only one position.
Edit: Image.
Assuming you have a MXN image. Create a mask for example
randi([-10 10], M , N)
Now add this to your original image. Now you get a new image whose all the pixels are modified but only within the range of -10 to 10. Some of the pixel values might go out of range in that case just modify as below
x(find(x < 0)) = 0 %Here X is your new image.
x(find(x > 255)) = 255