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Here is a solution that may work for some practical purposes. It uses numpy to have a quick vectorialized way to get a "big" array with 2D.

NROWS, NCOLS, WEIGHT = 24, 10, 5

z = np.zeros((NROWS - WEIGHT, NCOLS), dtype=np.int8)
u = np.ones ((              WEIGHT, NCOLS), dtype=np.int8)
a = np.concatenate((z, u), axis=0)

rng = np.random.default_rng()
b = rng.permuted(a, axis=0)

This initializes a matrix a with wanted blocks of zeros and ones,

sage: a
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=int8)

and we only need to scramble the columns. This can be done by using np.random.shuffle, but the simpler solution is to use the permuted method of the Generator type that came in one of the last versions of numpy (two or three years ago, i think).

And this time i've got for b:

sage: b
array([[0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 1, 1, 0, 1, 1, 0, 0, 0],
       [0, 1, 0, 0, 0, 0, 0, 1, 1, 0],
       [1, 0, 0, 0, 0, 0, 1, 1, 0, 1],
       [0, 1, 0, 1, 0, 0, 0, 1, 0, 0],
       [1, 0, 0, 1, 0, 1, 0, 1, 0, 1],
       [1, 0, 1, 0, 0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
       [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
       [1, 0, 1, 0, 0, 1, 1, 0, 1, 0],
       [0, 0, 0, 1, 1, 1, 0, 0, 0, 0],
       [0, 1, 0, 0, 0, 1, 0, 0, 0, 1],
       [0, 0, 0, 0, 1, 0, 0, 0, 1, 1],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
       [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
       [0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
       [0, 1, 1, 0, 1, 0, 0, 0, 1, 0],
       [1, 0, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=int8)