Lojban and Loglan are two related languages which have been created for this, focusing chiefly on syntactic ambiguity as well.
lˈɑːdʒbən ænd lˈɔɡlən ɑːɹ tˈuː ɹᵻlˈeɪɾᵻd lˈæŋɡwɪdʒᵻz wˌɪtʃ hɐvbɪn kɹiːˈeɪɾᵻd fɔːɹ ðˈɪs, fˈoʊkəsɪŋ tʃˈiːfli ˌɔn sɪntˈæktɪk ˌæmbɪɡjˈuːɪɾi æz wˈɛl.