The Court of Appeal’s decision to cut the jail term for a woman who killed three of her children and tried to murder another is being appealed by the Director of Public Prosecutions.

Akon Guode was last year jailed for 26 and a half years, with a minimum 20 years, for murdering her four-year-old twins, killing her 16-month-old son and trying to murder a fourth child by driving them into a Wyndham Vale lake in 2015.

Four-year-old twins Hangar and Madit and 16-month-old Bol all drowned, but their older sister, now eight, was rescued by residents and emergency service workers.

Guode appealed against her sentence and the Court of Appeal last month cut the jail term to 18 years. She must serve 14 years before she is eligible for parole.

Chief Justice Anne Ferguson found Guode’s state of mind was disturbed when she drove into the lake, as a result of the traumatic birth of her youngest child, Bol. Guode underwent life-saving surgery after Bol’s birth.

Chief Justice Ferguson and judges Phillip Priest and David Beach said they had not “lost sight of the fact that three vulnerable children lost their lives” and a fourth nearly did, but the Sudanese refugee’s situation was “pitiable”.

In war-torn Sudan, Guode saw her husband killed and was then raped until she was unconscious before fleeing in 2003 with three daughters to Uganda.

The appeal judges found Guode “fatefully and irredeemably breached” her children’s trust when she drove them into the lake, but “her capacity to make calm and rational decisions was severely compromised by a mental condition”.

On Friday, Director of Public Prosecutions Kerri Judd QC filed an application to appeal the decision to cut Guode’s sentence. Guode has already served three years, meaning she could be released in just over a decade although she faces being deported on release.

Guode pleaded guilty to two counts of murder, one of attempted murder and one of infanticide.