the problem sounds more like using the wrong approach to me. OP is selecting words at random instead of generating a random entropy then converting that to words. that is why he has only 121 bits of entropy not 128 (11 words * 11 bits).
the method should be generating 128 bits then converting that to words.

an alternative could be using the brute force as OP already guessed but from a starting point. meaning choose 12 words then change the last until the checksum is valid. that way the entropy size could actually be 132 bit (instead of 128).