The build-up construction over a commutative non-unital ring

There is a local ring I of order 4, without identity for the multiplication, defined by generators and relations as $$\begin{aligned} I=\langle a,b \mid 2a=2b=0,\, a^2=b,\, \,ab=0 \rangle . \end{aligned}$$ We study recursive construction self-orthogonal codes over I. classify self orthogonal length n size $$2^n$$ (called here quasi self-dual or QSD) up to $$n=6.$$ In particular, we Type IV (QSD with even weights) torsion code)