This is the code I used in the paper "Examples of special quadratic birational transformations into complete intersections of quadrics", https://doi.org/10.1016/j.jsc.2015.11.004, to construct some new examples of birational transformations of projective spaces whose base locus scheme is smooth and connected. The most relevant example is that of a Cremona transformation of P8 not defined along a smooth threefold scroll over a quintic del Pezzo surface.
Note that this is an old code, written in 2015 for Macaulay2 version 1.7. Today these examples can be easily obtained using the function specialQuadraticTransformation of the Macaulay2 package Cremona.