Tweed, the former partner of Goody, who died aged 27 of cervical cancer weeks after the couple got married in 2009, told the court: "I'm not making excuses, I've been through some trauma in my life, other stuff that led to me having depression and anxiety.
"I can't sleep at night, I'd found having a little bit of that helps me sleep through the night and that's what I was doing.
"I had some the night before to help me sleep again… stupid decision, I drove in the morning when I shouldn't have."
Wearing a black top, Tweed, of Buckhurst Hill, Essex, said he now works as an electrician, adding that his income varies and is "maybe £3,000 a month".
He added: "I've been working on myself, I've found other things to help myself get through situations and sleeping that doesn't involve drugs.
"I do work to keep my life in the forward motion – if I get banned it's just going to go backwards.
"I apologise, I'm sorry."
The court was told Tweed has seven previous convictions for 14 offences, including a conviction in 2007 for driving with excess alcohol.
Magistrate Andrew McGregor said Tweed would receive a statutory disqualification from driving of 12 months.
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